| version 1.8, 2001/07/03 01:41:26 |
version 1.10, 2018/03/29 01:32:51 |
|
|
| * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, |
* DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, |
| * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. |
* PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. |
| * |
* |
| * $OpenXM: OpenXM_contrib2/asir2000/engine/M.c,v 1.7 2001/06/25 04:11:42 noro Exp $ |
* $OpenXM: OpenXM_contrib2/asir2000/engine/M.c,v 1.9 2001/10/09 01:36:10 noro Exp $ |
| */ |
*/ |
| #include "ca.h" |
#include "ca.h" |
| #include "base.h" |
#include "base.h" |
| |
|
| void addum(mod,p1,p2,pr) |
void addum(int mod,UM p1,UM p2,UM pr) |
| int mod; |
|
| UM p1,p2,pr; |
|
| { |
{ |
| register int *c1,*c2,*cr,i,dmax,dmin; |
register int *c1,*c2,*cr,i,dmax,dmin; |
| |
|
| if ( DEG(p1) == -1 ) { |
if ( DEG(p1) == -1 ) { |
| cpyum(p2,pr); |
cpyum(p2,pr); |
| return; |
return; |
| } |
} |
| if ( DEG(p2) == -1 ) { |
if ( DEG(p2) == -1 ) { |
| cpyum(p1,pr); |
cpyum(p1,pr); |
| return; |
return; |
| } |
} |
| if ( DEG(p1) >= DEG(p2) ) { |
if ( DEG(p1) >= DEG(p2) ) { |
| c1 = COEF(p1); c2 = COEF(p2); dmax = DEG(p1); dmin = DEG(p2); |
c1 = COEF(p1); c2 = COEF(p2); dmax = DEG(p1); dmin = DEG(p2); |
| } else { |
} else { |
| c1 = COEF(p2); c2 = COEF(p1); dmax = DEG(p2); dmin = DEG(p1); |
c1 = COEF(p2); c2 = COEF(p1); dmax = DEG(p2); dmin = DEG(p1); |
| } |
} |
| for ( i = 0, cr = COEF(pr); i <= dmin; i++ ) |
for ( i = 0, cr = COEF(pr); i <= dmin; i++ ) |
| cr[i] = ( c1[i] + c2[i] ) % mod; |
cr[i] = ( c1[i] + c2[i] ) % mod; |
| for ( ; i <= dmax; i++ ) |
for ( ; i <= dmax; i++ ) |
| cr[i] = c1[i]; |
cr[i] = c1[i]; |
| if ( dmax == dmin ) |
if ( dmax == dmin ) |
| degum(pr,dmax); |
degum(pr,dmax); |
| else |
else |
| DEG(pr) = dmax; |
DEG(pr) = dmax; |
| } |
} |
| |
|
| void subum(mod,p1,p2,pr) |
void subum(int mod,UM p1,UM p2,UM pr) |
| int mod; |
|
| UM p1,p2,pr; |
|
| { |
{ |
| register int *c1,*c2,*cr,i; |
register int *c1,*c2,*cr,i; |
| int dmax,dmin; |
int dmax,dmin; |
| |
|
| if ( DEG(p1) == -1 ) { |
if ( DEG(p1) == -1 ) { |
| for ( i = DEG(pr) = DEG(p2), c2 = COEF(p2), cr = COEF(pr); |
for ( i = DEG(pr) = DEG(p2), c2 = COEF(p2), cr = COEF(pr); |
| i >= 0; i-- ) |
i >= 0; i-- ) |
| cr[i] = ( mod - c2[i] ) % mod; |
cr[i] = ( mod - c2[i] ) % mod; |
| return; |
return; |
| } |
} |
| if ( DEG(p2) == -1 ) { |
if ( DEG(p2) == -1 ) { |
| cpyum(p1,pr); |
cpyum(p1,pr); |
| return; |
return; |
| } |
} |
| c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr); |
c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr); |
| if ( DEG(p1) >= DEG(p2) ) { |
if ( DEG(p1) >= DEG(p2) ) { |
| dmax = DEG(p1); dmin = DEG(p2); |
dmax = DEG(p1); dmin = DEG(p2); |
| for ( i = 0; i <= dmin; i++ ) |
for ( i = 0; i <= dmin; i++ ) |
| cr[i] = ( c1[i] + mod - c2[i] ) % mod; |
cr[i] = ( c1[i] + mod - c2[i] ) % mod; |
| for ( ; i <= dmax; i++ ) |
for ( ; i <= dmax; i++ ) |
| cr[i] = c1[i]; |
cr[i] = c1[i]; |
| } else { |
} else { |
| dmax = DEG(p2); dmin = DEG(p1); |
dmax = DEG(p2); dmin = DEG(p1); |
| for ( i = 0; i <= dmin; i++ ) |
for ( i = 0; i <= dmin; i++ ) |
| cr[i] = ( c1[i] + mod - c2[i] ) % mod; |
cr[i] = ( c1[i] + mod - c2[i] ) % mod; |
| for ( ; i <= dmax; i++ ) |
for ( ; i <= dmax; i++ ) |
| cr[i] = ( mod - c2[i] ) % mod; |
cr[i] = ( mod - c2[i] ) % mod; |
| } |
} |
| if ( dmax == dmin ) |
if ( dmax == dmin ) |
| degum(pr,dmax); |
degum(pr,dmax); |
| else |
else |
| DEG(pr) = dmax; |
DEG(pr) = dmax; |
| } |
} |
| |
|
| void pwrum(mod,p,e,pr) |
void pwrum(int mod,UM p,int e,UM pr) |
| int mod,e; |
|
| UM p,pr; |
|
| { |
{ |
| UM wt,ws; |
UM wt,ws; |
| |
|
| if ( e == 0 ) { |
if ( e == 0 ) { |
| DEG(pr) = 0; COEF(pr)[0] = 1; |
DEG(pr) = 0; COEF(pr)[0] = 1; |
| } else if ( DEG(p) < 0 ) |
} else if ( DEG(p) < 0 ) |
| DEG(pr) = -1; |
DEG(pr) = -1; |
| else if ( e == 1 ) |
else if ( e == 1 ) |
| cpyum(p,pr); |
cpyum(p,pr); |
| else if ( DEG(p) == 0 ) { |
else if ( DEG(p) == 0 ) { |
| DEG(pr) = 0; COEF(pr)[0] = pwrm(mod,COEF(p)[0],e); |
DEG(pr) = 0; COEF(pr)[0] = pwrm(mod,COEF(p)[0],e); |
| } else { |
} else { |
| wt = W_UMALLOC(DEG(p)*e); ws = W_UMALLOC(DEG(p)*e); |
wt = W_UMALLOC(DEG(p)*e); ws = W_UMALLOC(DEG(p)*e); |
| pwrum(mod,p,e/2,wt); |
pwrum(mod,p,e/2,wt); |
| if ( !(e%2) ) |
if ( !(e%2) ) |
| mulum(mod,wt,wt,pr); |
mulum(mod,wt,wt,pr); |
| else { |
else { |
| mulum(mod,wt,wt,ws); mulum(mod,ws,p,pr); |
mulum(mod,wt,wt,ws); mulum(mod,ws,p,pr); |
| } |
} |
| } |
} |
| } |
} |
| |
|
| void gcdum(mod,p1,p2,pr) |
void gcdum(int mod,UM p1,UM p2,UM pr) |
| register int mod; |
|
| UM p1,p2,pr; |
|
| { |
{ |
| register int inv; |
register int inv; |
| UM t1,t2,q,tum; |
UM t1,t2,q,tum; |
| int drem; |
int drem; |
| |
|
| if ( DEG(p1) < 0 ) |
if ( DEG(p1) < 0 ) |
| cpyum(p2,pr); |
cpyum(p2,pr); |
| else if ( DEG(p2) < 0 ) |
else if ( DEG(p2) < 0 ) |
| cpyum(p1,pr); |
cpyum(p1,pr); |
| else { |
else { |
| if ( DEG(p1) >= DEG(p2) ) { |
if ( DEG(p1) >= DEG(p2) ) { |
| t1 = p1; t2 = p2; |
t1 = p1; t2 = p2; |
| } else { |
} else { |
| t1 = p2; t2 = p1; |
t1 = p2; t2 = p1; |
| } |
} |
| q = W_UMALLOC(DEG(t1)); |
q = W_UMALLOC(DEG(t1)); |
| while ( ( drem = divum(mod,t1,t2,q) ) >= 0 ) { |
while ( ( drem = divum(mod,t1,t2,q) ) >= 0 ) { |
| tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem; |
tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem; |
| } |
} |
| inv = invm(COEF(t2)[DEG(t2)],mod); |
inv = invm(COEF(t2)[DEG(t2)],mod); |
| mulsum(mod,t2,inv,pr); |
mulsum(mod,t2,inv,pr); |
| } |
} |
| } |
} |
| |
|
| void eucum(mod,f1,f2,a,b) |
void eucum(int mod,UM f1,UM f2,UM a,UM b) |
| register int mod; |
|
| UM f1,f2,a,b; |
|
| { |
{ |
| UM g1,g2,a1,a2,a3,wm,q,tum; |
UM g1,g2,a1,a2,a3,wm,q,tum; |
| int d,dr; |
int d,dr; |
| UM t1,t2,t3; |
|
| |
|
| d = DEG(f1) + DEG(f2) + 10; |
d = DEG(f1) + DEG(f2) + 10; |
| g1 = W_UMALLOC(d); g2 = W_UMALLOC(d); a1 = W_UMALLOC(d); |
g1 = W_UMALLOC(d); g2 = W_UMALLOC(d); a1 = W_UMALLOC(d); |
| a2 = W_UMALLOC(d); a3 = W_UMALLOC(d); wm = W_UMALLOC(d); |
a2 = W_UMALLOC(d); a3 = W_UMALLOC(d); wm = W_UMALLOC(d); |
| q = W_UMALLOC(d); |
q = W_UMALLOC(d); |
| DEG(a1) = 0; COEF(a1)[0] = 1; DEG(a2) = -1; |
DEG(a1) = 0; COEF(a1)[0] = 1; DEG(a2) = -1; |
| cpyum(f1,g1); cpyum(f2,g2); |
cpyum(f1,g1); cpyum(f2,g2); |
| while ( 1 ) { |
while ( 1 ) { |
| dr = divum(mod,g1,g2,q); tum = g1; g1 = g2; g2 = tum; |
dr = divum(mod,g1,g2,q); tum = g1; g1 = g2; g2 = tum; |
| if ( ( DEG(g2) = dr ) == -1 ) |
if ( ( DEG(g2) = dr ) == -1 ) |
| break; |
break; |
| mulum(mod,a2,q,wm); subum(mod,a1,wm,a3); dr = divum(mod,a3,f2,q); |
mulum(mod,a2,q,wm); subum(mod,a1,wm,a3); dr = divum(mod,a3,f2,q); |
| tum = a1; a1 = a2; a2 = a3; a3 = tum; DEG(a3) = dr; |
tum = a1; a1 = a2; a2 = a3; a3 = tum; DEG(a3) = dr; |
| } |
} |
| if ( COEF(g1)[0] != 1 ) |
if ( COEF(g1)[0] != 1 ) |
| mulsum(mod,a2,invm(COEF(g1)[0],mod),a); |
mulsum(mod,a2,invm(COEF(g1)[0],mod),a); |
| else |
else |
| cpyum(a2,a); |
cpyum(a2,a); |
| mulum(mod,a,f1,wm); |
mulum(mod,a,f1,wm); |
| if ( DEG(wm) >= 0 ) |
if ( DEG(wm) >= 0 ) |
| COEF(wm)[0] = ( COEF(wm)[0] + mod - 1 ) % mod; |
COEF(wm)[0] = ( COEF(wm)[0] + mod - 1 ) % mod; |
| else { |
else { |
| DEG(wm) = 0; COEF(wm)[0] = mod - 1; |
DEG(wm) = 0; COEF(wm)[0] = mod - 1; |
| } |
} |
| divum(mod,wm,f2,q); mulsum(mod,q,mod-1,b); |
divum(mod,wm,f2,q); mulsum(mod,q,mod-1,b); |
| #if 0 |
#if 0 |
| t1 = W_UMALLOC(d); |
t1 = W_UMALLOC(d); |
| t2 = W_UMALLOC(d); |
t2 = W_UMALLOC(d); |
| t3 = W_UMALLOC(d); |
t3 = W_UMALLOC(d); |
| mulum(mod,a,f1,t1); |
mulum(mod,a,f1,t1); |
| mulum(mod,b,f2,t2); |
mulum(mod,b,f2,t2); |
| addum(mod,t1,t2,t3); |
addum(mod,t1,t2,t3); |
| #endif |
#endif |
| } |
} |
| |
|
| void eucum2(mod,f1,f2,a,b) |
void eucum2(int mod,UM f1,UM f2,UM a,UM b) |
| register int mod; |
|
| UM f1,f2,a,b; |
|
| { |
{ |
| UM gk,gk1,gk2,ak,ak1,ak2,bk,bk1,bk2,q,t,wm1,wm2,wz; |
UM gk,gk1,gk2,ak,ak1,ak2,bk,bk1,bk2,q,t,wm1,wm2,wz; |
| int d,inv; |
int d,inv; |
| UM t1,t2; |
UM t1,t2; |
| |
|
| d = 2*(DEG(f1) + DEG(f2)); |
d = 2*(DEG(f1) + DEG(f2)); |
| gk = W_UMALLOC(d); gk1 = W_UMALLOC(d); gk2 = W_UMALLOC(d); |
gk = W_UMALLOC(d); gk1 = W_UMALLOC(d); gk2 = W_UMALLOC(d); |
| ak = W_UMALLOC(d); ak1 = W_UMALLOC(d); ak2 = W_UMALLOC(d); |
ak = W_UMALLOC(d); ak1 = W_UMALLOC(d); ak2 = W_UMALLOC(d); |
| bk = W_UMALLOC(d); bk1 = W_UMALLOC(d); bk2 = W_UMALLOC(d); |
bk = W_UMALLOC(d); bk1 = W_UMALLOC(d); bk2 = W_UMALLOC(d); |
| q = W_UMALLOC(d); wm1 = W_UMALLOC(d); wm2 = W_UMALLOC(d); |
q = W_UMALLOC(d); wm1 = W_UMALLOC(d); wm2 = W_UMALLOC(d); |
| wz = W_UMALLOC(d); |
wz = W_UMALLOC(d); |
| |
|
| t1 = UMALLOC(1000); |
t1 = UMALLOC(1000); |
| t2 = UMALLOC(1000); |
t2 = UMALLOC(1000); |
| cpyum(f1,t1); |
cpyum(f1,t1); |
| cpyum(f2,t2); |
cpyum(f2,t2); |
| |
|
| DEG(ak) = 0; COEF(ak)[0] = 1; |
DEG(ak) = 0; COEF(ak)[0] = 1; |
| DEG(ak1) = -1; |
DEG(ak1) = -1; |
| DEG(bk) = -1; |
DEG(bk) = -1; |
| DEG(bk1) = 0; COEF(bk1)[0] = 1; |
DEG(bk1) = 0; COEF(bk1)[0] = 1; |
| |
|
| cpyum(f1,gk); cpyum(f2,gk1); |
cpyum(f1,gk); cpyum(f2,gk1); |
| |
|
| while ( 1 ) { |
while ( 1 ) { |
| /* ak*f1+bk*f2 = gk, ak1*f1+bk1*f2 = gk1 */ |
/* ak*f1+bk*f2 = gk, ak1*f1+bk1*f2 = gk1 */ |
| cpyum(gk,gk2); |
cpyum(gk,gk2); |
| DEG(gk2) = divum(mod,gk2,gk1,q); |
DEG(gk2) = divum(mod,gk2,gk1,q); |
| /* gk2 = gk - q*gk1 */ |
/* gk2 = gk - q*gk1 */ |
| if ( DEG(gk2) == -1 ) |
if ( DEG(gk2) == -1 ) |
| break; |
break; |
| /* ak2 = ak - q*ak1, bk2 = bk - q*bk1 */ |
/* ak2 = ak - q*ak1, bk2 = bk - q*bk1 */ |
| mulum(mod,ak1,q,wm1); subum(mod,ak,wm1,ak2); |
mulum(mod,ak1,q,wm1); subum(mod,ak,wm1,ak2); |
| mulum(mod,bk1,q,wm1); subum(mod,bk,wm1,bk2); |
mulum(mod,bk1,q,wm1); subum(mod,bk,wm1,bk2); |
| |
|
| /* shift */ |
/* shift */ |
| t = ak; ak = ak1; ak1 = ak2; ak2 = t; |
t = ak; ak = ak1; ak1 = ak2; ak2 = t; |
| t = bk; bk = bk1; bk1 = bk2; bk2 = t; |
t = bk; bk = bk1; bk1 = bk2; bk2 = t; |
| t = gk; gk = gk1; gk1 = gk2; gk2 = t; |
t = gk; gk = gk1; gk1 = gk2; gk2 = t; |
| } |
} |
| /* ak1*f1+bk1*f2 = gk1 = GCD(f1,f2) */ |
/* ak1*f1+bk1*f2 = gk1 = GCD(f1,f2) */ |
| mulum(mod,ak1,t1,wm1); |
mulum(mod,ak1,t1,wm1); |
| mulum(mod,bk1,t2,wm2); |
mulum(mod,bk1,t2,wm2); |
| addum(mod,wm1,wm2,wz); |
addum(mod,wm1,wm2,wz); |
| if ( DEG(wz) != 0 ) |
if ( DEG(wz) != 0 ) |
| error("euc 1"); |
error("euc 1"); |
| |
|
| DEG(ak1) = divum(mod,ak1,f2,q); |
DEG(ak1) = divum(mod,ak1,f2,q); |
| DEG(bk1) = divum(mod,bk1,f1,q); |
DEG(bk1) = divum(mod,bk1,f1,q); |
| mulum(mod,ak1,f1,wm1); |
mulum(mod,ak1,f1,wm1); |
| mulum(mod,bk1,f2,wm2); |
mulum(mod,bk1,f2,wm2); |
| addum(mod,wm1,wm2,wz); |
addum(mod,wm1,wm2,wz); |
| if ( DEG(wz) != 0 ) |
if ( DEG(wz) != 0 ) |
| error("euc 2"); |
error("euc 2"); |
| |
|
| |
|
| if ( COEF(wz)[0] != 1 ) { |
if ( COEF(wz)[0] != 1 ) { |
| inv = invm(COEF(wz)[0],mod); |
inv = invm(COEF(wz)[0],mod); |
| mulsum(mod,ak1,inv,a); |
mulsum(mod,ak1,inv,a); |
| mulsum(mod,bk1,inv,b); |
mulsum(mod,bk1,inv,b); |
| } else { |
} else { |
| cpyum(ak1,a); |
cpyum(ak1,a); |
| cpyum(bk1,b); |
cpyum(bk1,b); |
| } |
} |
| } |
} |
| |
|
| void sqfrum(index,count,f,nindex,dcr,pl) |
void sqfrum(int index,int count,P f,int *nindex,struct oDUM **dcr,ML *pl) |
| int index,count,*nindex; |
|
| P f; |
|
| struct oDUM **dcr; |
|
| ML *pl; |
|
| { |
{ |
| int i,j,m,n,d,dt,mod; |
int i,j,m,n,d,dt,mod; |
| UM wf,wdf,ws,wt,wgcd,mf,mgcd; |
UM wf,wdf,ws,wt,wgcd,mf,mgcd; |
| UM *l; |
UM *l; |
| struct oDUM *dc; |
struct oDUM *dc; |
| ML tp; |
ML tp; |
| |
|
| n = UDEG(f); |
n = UDEG(f); |
| wf = W_UMALLOC(n); |
wf = W_UMALLOC(n); |
| wdf = W_UMALLOC(n); |
wdf = W_UMALLOC(n); |
| ws = W_UMALLOC(n); |
ws = W_UMALLOC(n); |
| wt = W_UMALLOC(n); |
wt = W_UMALLOC(n); |
| wgcd = W_UMALLOC(n); |
wgcd = W_UMALLOC(n); |
| |
|
| mf = W_UMALLOC(n); |
mf = W_UMALLOC(n); |
| mgcd = W_UMALLOC(n); |
mgcd = W_UMALLOC(n); |
| |
|
| for ( j = 0, d = n; j < count && d; ) { |
for ( j = 0, d = n; j < count && d; ) { |
| m = get_lprime(index++); |
m = get_lprime(index++); |
| if ( rem(NM((Q)COEF(DC(f))),m) == 0 ) continue; |
if ( rem(NM((Q)COEF(DC(f))),m) == 0 ) continue; |
| |
|
| ptoum(m,f,wf); |
ptoum(m,f,wf); |
| diffum(m,wf,wdf); |
diffum(m,wf,wdf); |
| cpyum(wf,wt); cpyum(wdf,ws); |
cpyum(wf,wt); cpyum(wdf,ws); |
| gcdum(m,wt,ws,wgcd); |
gcdum(m,wt,ws,wgcd); |
| dt = DEG(wgcd); |
dt = DEG(wgcd); |
| |
|
| if ( dt < d ) { |
if ( dt < d ) { |
| d = dt; |
d = dt; |
| mod = m; |
mod = m; |
| cpyum(wf,mf); cpyum(wgcd,mgcd); |
cpyum(wf,mf); cpyum(wgcd,mgcd); |
| } |
} |
| j++; |
j++; |
| } |
} |
| *nindex = index; |
*nindex = index; |
| |
|
| sqfrummain(mod,mf,mgcd,&dc); |
sqfrummain(mod,mf,mgcd,&dc); |
| *dcr = dc; |
*dcr = dc; |
| |
|
| for ( n = 0; dc[n].f; n++ ); |
for ( n = 0; dc[n].f; n++ ); |
| *pl = tp = MLALLOC(n+1); |
*pl = tp = MLALLOC(n+1); |
| tp->n = n; |
tp->n = n; |
| tp->mod = mod; |
tp->mod = mod; |
| |
|
| for ( i = 0, l = (UM *)COEF(tp); dc[i].f; i++ ) { |
for ( i = 0, l = (UM *)COEF(tp); dc[i].f; i++ ) { |
| l[i] = UMALLOC(DEG(dc[i].f)*dc[i].n); |
l[i] = UMALLOC(DEG(dc[i].f)*dc[i].n); |
| pwrum(mod,dc[i].f,dc[i].n,l[i]); |
pwrum(mod,dc[i].f,dc[i].n,l[i]); |
| } |
} |
| l[i] = 0; |
l[i] = 0; |
| } |
} |
| |
|
| void sqfrummain(mod,p,gcd,dcp) |
void sqfrummain(int mod,UM p,UM gcd,struct oDUM **dcp) |
| int mod; |
|
| UM p,gcd; |
|
| struct oDUM **dcp; |
|
| { |
{ |
| int i,j,n; |
int i,j,n; |
| UM wp,wdp,wc,wd,ws,wt,wq; |
UM wp,wdp,wc,wd,ws,wt,wq; |
| struct oDUM *dc; |
struct oDUM *dc; |
| UM *f; |
UM *f; |
| |
|
| i = DEG(p); |
i = DEG(p); |
| |
|
| wp = W_UMALLOC(i); |
wp = W_UMALLOC(i); |
| wdp = W_UMALLOC(i); |
wdp = W_UMALLOC(i); |
| wt = W_UMALLOC(i); |
wt = W_UMALLOC(i); |
| ws = W_UMALLOC(i); |
ws = W_UMALLOC(i); |
| wc = W_UMALLOC(i); |
wc = W_UMALLOC(i); |
| wd = W_UMALLOC(i); |
wd = W_UMALLOC(i); |
| wq = W_UMALLOC(i); |
wq = W_UMALLOC(i); |
| |
|
| f = (UM *) ALLOCA((i+2)*sizeof(UM)); |
f = (UM *) ALLOCA((i+2)*sizeof(UM)); |
| |
|
| cpyum(p,wp); |
cpyum(p,wp); |
| diffum(mod,wp,wdp); |
diffum(mod,wp,wdp); |
| |
|
| cpyum(wp,wt); |
cpyum(wp,wt); |
| divum(mod,wt,gcd,wc); |
divum(mod,wt,gcd,wc); |
| |
|
| cpyum(wdp,wt); |
cpyum(wdp,wt); |
| divum(mod,wt,gcd,ws); |
divum(mod,wt,gcd,ws); |
| |
|
| diffum(mod,wc,wt); |
diffum(mod,wc,wt); |
| subum(mod,ws,wt,wd); |
subum(mod,ws,wt,wd); |
| |
|
| for ( i = 1; DEG(wd) >= 0; i++ ) { |
for ( i = 1; DEG(wd) >= 0; i++ ) { |
| cpyum(wc,ws); cpyum(wd,wt); |
cpyum(wc,ws); cpyum(wd,wt); |
| gcdum(mod,ws,wt,wq); |
gcdum(mod,ws,wt,wq); |
| if ( DEG(wq) > 0 ) { |
if ( DEG(wq) > 0 ) { |
| f[i] = UMALLOC(DEG(wq)); |
f[i] = UMALLOC(DEG(wq)); |
| cpyum(wq,f[i]); |
cpyum(wq,f[i]); |
| |
|
| cpyum(wc,ws); |
cpyum(wc,ws); |
| divum(mod,ws,f[i],wc); |
divum(mod,ws,f[i],wc); |
| divum(mod,wd,f[i],ws); |
divum(mod,wd,f[i],ws); |
| diffum(mod,wc,wt); |
diffum(mod,wc,wt); |
| subum(mod,ws,wt,wd); |
subum(mod,ws,wt,wd); |
| } else { |
} else { |
| f[i] = 0; |
f[i] = 0; |
| cpyum(wd,ws); |
cpyum(wd,ws); |
| diffum(mod,wc,wt); |
diffum(mod,wc,wt); |
| subum(mod,ws,wt,wd); |
subum(mod,ws,wt,wd); |
| } |
} |
| |
|
| } |
} |
| |
|
| if ( DEG(wc) > 0 ) { |
if ( DEG(wc) > 0 ) { |
| DEG(wq) = 0; |
DEG(wq) = 0; |
| COEF(wq)[0] = invm(COEF(wc)[DEG(wc)],mod); |
COEF(wq)[0] = invm(COEF(wc)[DEG(wc)],mod); |
| f[i] = UMALLOC(DEG(wc)); |
f[i] = UMALLOC(DEG(wc)); |
| mulum(mod,wc,wq,f[i]); |
mulum(mod,wc,wq,f[i]); |
| f[i+1] = 0; |
f[i+1] = 0; |
| n = i + 1; |
n = i + 1; |
| } else { |
} else { |
| f[i] = 0; |
f[i] = 0; |
| n = i; |
n = i; |
| } |
} |
| |
|
| for ( i = 1, j = 0; i < n; i++ ) |
for ( i = 1, j = 0; i < n; i++ ) |
| if ( f[i] ) j++; |
if ( f[i] ) j++; |
| |
|
| *dcp = dc = (struct oDUM *) CALLOC(j+1,sizeof(struct oDUM)); |
*dcp = dc = (struct oDUM *) CALLOC(j+1,sizeof(struct oDUM)); |
| |
|
| for ( i = 1, j = 0; i < n; i++ ) |
for ( i = 1, j = 0; i < n; i++ ) |
| if ( f[i] ) { |
if ( f[i] ) { |
| dc[j].n = i; |
dc[j].n = i; |
| dc[j].f = f[i]; |
dc[j].f = f[i]; |
| j++; |
j++; |
| } |
} |
| dc[j].n = 0; |
dc[j].n = 0; |
| dc[j].f = 0; |
dc[j].f = 0; |
| } |
} |
| |
|
| void cpyum(p1,p2) |
void cpyum(UM p1,UM p2) |
| UM p1,p2; |
|
| { |
{ |
| register int *c1,*c2,i; |
register int *c1,*c2,i; |
| |
|
| for ( i = DEG(p2) = DEG(p1), c1 = COEF(p1), c2 = COEF(p2); |
for ( i = DEG(p2) = DEG(p1), c1 = COEF(p1), c2 = COEF(p2); |
| i >= 0; i-- ) |
i >= 0; i-- ) |
| c2[i] = c1[i]; |
c2[i] = c1[i]; |
| } |
} |
| |
|
| void clearum(p,n) |
void clearum(UM p,int n) |
| UM p; |
|
| int n; |
|
| { |
{ |
| DEG(p) = -1; |
DEG(p) = -1; |
| bzero(COEF(p),(n+1)*sizeof(int)); |
bzero(COEF(p),(n+1)*sizeof(int)); |
| } |
} |
| |
|
| void degum(f,n) |
void degum(UM f,int n) |
| UM f; |
|
| int n; |
|
| { |
{ |
| register int i,*c; |
register int i,*c; |
| |
|
| for ( i = n, c = COEF(f); ( i >= 0 ) && ( c[i] == 0 ); i-- ); |
for ( i = n, c = COEF(f); ( i >= 0 ) && ( c[i] == 0 ); i-- ); |
| DEG(f) = i; |
DEG(f) = i; |
| } |
} |
| |
|
| int deg(v,p) |
int deg(V v,P p) |
| V v; |
|
| P p; |
|
| { |
{ |
| if ( !p ) |
if ( !p ) |
| return ( -1 ); |
return ( -1 ); |
| else if ( NUM(p) ) |
else if ( NUM(p) ) |
| return ( 0 ); |
return ( 0 ); |
| else if ( VR(p) != v ) |
else if ( VR(p) != v ) |
| return ( 0 ); |
return ( 0 ); |
| else if ( PL(NM(DEG(DC(p)))) > 1 ) { |
else if ( PL(NM(DEG(DC(p)))) > 1 ) { |
| error("degree too large"); |
error("degree too large"); |
| return ( -1 ); |
return ( -1 ); |
| } else |
} else |
| return ( UDEG(p) ); |
return ( UDEG(p) ); |
| } |
} |
| |
|
| LUM LUMALLOC(n,bound) |
LUM LUMALLOC(int n,int bound) |
| int n,bound; |
|
| { |
{ |
| LUM p; |
LUM p; |
| int **c; |
int **c; |
| int i; |
int i; |
| |
|
| p = (LUM)MALLOC(TRUESIZE(oLUM,n,int *)); |
p = (LUM)MALLOC(TRUESIZE(oLUM,n,int *)); |
| DEG(p) = n; |
DEG(p) = n; |
| for ( i = 0, c = (int **)COEF(p); i <= n; i++ ) { |
for ( i = 0, c = (int **)COEF(p); i <= n; i++ ) { |
| c[i] = (int *)MALLOC_ATOMIC((bound+1)*sizeof(int)); |
c[i] = (int *)MALLOC_ATOMIC((bound+1)*sizeof(int)); |
| bzero((char *)c[i],(bound+1)*sizeof(int)); |
bzero((char *)c[i],(bound+1)*sizeof(int)); |
| } |
} |
| return p; |
return p; |
| } |
} |
| |
|
| /* dx = deg in x, dy = deg in y, c[i] <-> the coef of y^i (poly in x) */ |
/* dx = deg in x, dy = deg in y, c[i] <-> the coef of y^i (poly in x) */ |
| |
|
| BM BMALLOC(dx,dy) |
BM BMALLOC(int dx,int dy) |
| int dx,dy; |
|
| { |
{ |
| BM p; |
BM p; |
| UM *c; |
UM *c; |
| int i; |
int i; |
| |
|
| p = (BM)MALLOC(TRUESIZE(oBM,dy,UM)); |
p = (BM)MALLOC(TRUESIZE(oBM,dy,UM)); |
| DEG(p) = dy; |
DEG(p) = dy; |
| for ( i = 0, c = (UM *)COEF(p); i <= dy; i++ ) { |
for ( i = 0, c = (UM *)COEF(p); i <= dy; i++ ) { |
| c[i] = UMALLOC(dx); |
c[i] = UMALLOC(dx); |
| clearum(c[i],dx); |
clearum(c[i],dx); |
| } |
} |
| return p; |
return p; |
| } |
} |
| |
|
| void mullum(mod,n,f1,f2,fr) |
void mullum(int mod,int n,LUM f1,LUM f2,LUM fr) |
| int mod,n; |
|
| LUM f1,f2,fr; |
|
| { |
{ |
| int max; |
int max; |
| register int i,j,**p1,**p2,*px; |
register int i,j,**p1,**p2,*px; |
| int *w,*w1,*w2; |
int *w,*w1,*w2; |
| |
|
| p1 = (int **)COEF(f1); p2 = (int **)COEF(f2); |
p1 = (int **)COEF(f1); p2 = (int **)COEF(f2); |
| w = W_ALLOC(2*(n+1)); w1 = W_ALLOC(DEG(f1)); w2 = W_ALLOC(DEG(f2)); |
w = W_ALLOC(2*(n+1)); w1 = W_ALLOC(DEG(f1)); w2 = W_ALLOC(DEG(f2)); |
| for ( i = DEG(f1); i >= 0; i-- ) { |
for ( i = DEG(f1); i >= 0; i-- ) { |
| for ( j = n - 1, px = p1[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- ); |
for ( j = n - 1, px = p1[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- ); |
| w1[i] = ( j == -1 ? 0 : 1 ); |
w1[i] = ( j == -1 ? 0 : 1 ); |
| } |
} |
| for ( i = DEG(f2); i >= 0; i-- ) { |
for ( i = DEG(f2); i >= 0; i-- ) { |
| for ( j = n - 1, px = p2[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- ); |
for ( j = n - 1, px = p2[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- ); |
| w2[i] = ( j == -1 ? 0 : 1 ); |
w2[i] = ( j == -1 ? 0 : 1 ); |
| } |
} |
| for ( j = DEG(fr) = DEG(f1) + DEG(f2); j >= 0; j-- ) { |
for ( j = DEG(fr) = DEG(f1) + DEG(f2); j >= 0; j-- ) { |
| for ( i = n - 1, px = COEF(fr)[j]; i >= 0; i-- ) |
for ( i = n - 1, px = COEF(fr)[j]; i >= 0; i-- ) |
| px[i] = 0; |
px[i] = 0; |
| for ( max = MIN(DEG(f1),j), i = MAX(0,j-DEG(f2)); i <= max; i++ ) |
for ( max = MIN(DEG(f1),j), i = MAX(0,j-DEG(f2)); i <= max; i++ ) |
| if ( w1[i] != 0 && w2[j - i] != 0 ) { |
if ( w1[i] != 0 && w2[j - i] != 0 ) { |
| mulpadic(mod,n,p1[i],p2[j - i],w); addpadic(mod,n,w,px); |
mulpadic(mod,n,p1[i],p2[j - i],w); addpadic(mod,n,w,px); |
| } |
} |
| } |
} |
| } |
} |
| |
|
| void cpylum(bound,p,r) |
void cpylum(int bound,LUM p,LUM r) |
| int bound; |
|
| LUM p,r; |
|
| { |
{ |
| register int i,j; |
register int i,j; |
| register int **pp,**ppr; |
register int **pp,**ppr; |
| |
|
| DEG(r) = DEG(p); |
DEG(r) = DEG(p); |
| for ( i = 0, pp = COEF(p), ppr = COEF(r); |
for ( i = 0, pp = COEF(p), ppr = COEF(r); |
| i <= DEG(p); i++ ) |
i <= DEG(p); i++ ) |
| for ( j = 0; j < bound; j++ ) |
for ( j = 0; j < bound; j++ ) |
| ppr[i][j] = pp[i][j]; |
ppr[i][j] = pp[i][j]; |
| } |
} |
| |
|
| int isequalum(f1,f2) |
int isequalum(UM f1,UM f2) |
| UM f1,f2; |
|
| { |
{ |
| int i; |
int i; |
| |
|
| if ( DEG(f1) < 0 ) |
if ( DEG(f1) < 0 ) |
| if ( DEG(f2) < 0 ) |
if ( DEG(f2) < 0 ) |
| return 1; |
return 1; |
| else |
else |
| return 0; |
return 0; |
| else if ( DEG(f2) < 0 ) |
else if ( DEG(f2) < 0 ) |
| return 0; |
return 0; |
| else { |
else { |
| if ( DEG(f1) != DEG(f2) ) |
if ( DEG(f1) != DEG(f2) ) |
| return 0; |
return 0; |
| for ( i = 0; i <= DEG(f1); i++ ) |
for ( i = 0; i <= DEG(f1); i++ ) |
| if ( COEF(f1)[i] != COEF(f2)[i] ) |
if ( COEF(f1)[i] != COEF(f2)[i] ) |
| break; |
break; |
| if ( i < DEG(f1) ) |
if ( i < DEG(f1) ) |
| return 0; |
return 0; |
| else |
else |
| return 1; |
return 1; |
| } |
} |
| } |
} |
| |
|
| void pwrlum(mod,bound,p,n,r) |
void pwrlum(int mod,int bound,LUM p,int n,LUM r) |
| int mod,bound,n; |
|
| LUM p,r; |
|
| { |
{ |
| LUM t,s; |
LUM t,s; |
| |
|
| if ( n == 0 ) { |
if ( n == 0 ) { |
| DEG(r) = 0; |
DEG(r) = 0; |
| COEF(r)[0][0] = 1; |
COEF(r)[0][0] = 1; |
| } else if ( DEG(p) < 0 ) |
} else if ( DEG(p) < 0 ) |
| DEG(r) = -1; |
DEG(r) = -1; |
| else if ( n == 1 ) |
else if ( n == 1 ) |
| cpylum(bound,p,r); |
cpylum(bound,p,r); |
| else { |
else { |
| W_LUMALLOC(DEG(p)*n,bound,t); |
W_LUMALLOC(DEG(p)*n,bound,t); |
| pwrlum(mod,bound,p,n/2,t); |
pwrlum(mod,bound,p,n/2,t); |
| if ( !(n%2) ) |
if ( !(n%2) ) |
| mullum(mod,bound,t,t,r); |
mullum(mod,bound,t,t,r); |
| else { |
else { |
| W_LUMALLOC(DEG(p)*n,bound,s); |
W_LUMALLOC(DEG(p)*n,bound,s); |
| mullum(mod,bound,t,t,s); |
mullum(mod,bound,t,t,s); |
| mullum(mod,bound,s,p,r); |
mullum(mod,bound,s,p,r); |
| } |
} |
| } |
} |
| } |
} |
| |
|
| int **almat(n,m) |
int **almat(int n,int m) |
| int n,m; |
|
| { |
{ |
| int **mat,i; |
int **mat,i; |
| |
|
| mat = (int **)MALLOC(n*sizeof(int *)); |
mat = (int **)MALLOC(n*sizeof(int *)); |
| for ( i = 0; i < n; i++ ) |
for ( i = 0; i < n; i++ ) |
| mat[i] = (int *)CALLOC(m,sizeof(int)); |
mat[i] = (int *)CALLOC(m,sizeof(int)); |
| return mat; |
return mat; |
| } |
} |
| |
|
| void mini(mod,f,fr) |
void mini(int mod,UM f,UM fr) |
| register int mod; |
|
| UM f,fr; |
|
| { |
{ |
| register int i,j,**c,*ptr; |
register int i,j,**c,*ptr; |
| int d,dr,dm,n; |
int d,dr,dm,n; |
| UM w,q; |
UM w,q; |
| |
|
| n = DEG(f); c = (int **)ALLOCA(n*sizeof(int *)); |
n = DEG(f); c = (int **)ALLOCA(n*sizeof(int *)); |
| for ( i = 0; i < n; i++ ) { |
for ( i = 0; i < n; i++ ) { |
| c[i] = (int *)ALLOCA(n*sizeof(int)); |
c[i] = (int *)ALLOCA(n*sizeof(int)); |
| bzero((char *)c[i],(int)(n*sizeof(int))); |
bzero((char *)c[i],(int)(n*sizeof(int))); |
| } |
} |
| w = W_UMALLOC( mod + n + 10 ); q = W_UMALLOC( mod + n + 10 ); |
w = W_UMALLOC( mod + n + 10 ); q = W_UMALLOC( mod + n + 10 ); |
| for ( i = 1; ( d = ( mod * i ) ) < n; i++ ) c[d][i - 1] = 1; |
for ( i = 1; ( d = ( mod * i ) ) < n; i++ ) c[d][i - 1] = 1; |
| DEG(w) = d; |
DEG(w) = d; |
| for ( j = 0; j < d; j++ ) |
for ( j = 0; j < d; j++ ) |
| COEF(w)[j] = 0; |
COEF(w)[j] = 0; |
| COEF(w)[d] = 1; |
COEF(w)[d] = 1; |
| for ( ; (i < n) && ((dr = divum(mod,w,f,q)) >= 0); i++ ) { |
for ( ; (i < n) && ((dr = divum(mod,w,f,q)) >= 0); i++ ) { |
| for ( j = dr; j >= 0; j-- ) |
for ( j = dr; j >= 0; j-- ) |
| COEF(w)[j + mod] = c[j][i - 1] = COEF(w)[j]; |
COEF(w)[j + mod] = c[j][i - 1] = COEF(w)[j]; |
| for ( j = mod - 1; j >= 0; j-- ) |
for ( j = mod - 1; j >= 0; j-- ) |
| COEF(w)[j] = 0; |
COEF(w)[j] = 0; |
| DEG(w) = dr + mod; |
DEG(w) = dr + mod; |
| } |
} |
| for ( i = 1; i < n; i++ ) |
for ( i = 1; i < n; i++ ) |
| c[i][i - 1] = ( c[i][i - 1] + mod - 1 ) % mod; |
c[i][i - 1] = ( c[i][i - 1] + mod - 1 ) % mod; |
| if ( ( dm = minimain(mod,n,n - 1,c) ) != -1 ) |
if ( ( dm = minimain(mod,n,n - 1,c) ) != -1 ) |
| for ( i = 0, ptr = COEF(fr), ptr[0] = 0; i <= dm; i++ ) |
for ( i = 0, ptr = COEF(fr), ptr[0] = 0; i <= dm; i++ ) |
| ptr[i + 1] = c[0][i]; |
ptr[i + 1] = c[0][i]; |
| else |
else |
| COEF(fr)[0] = 1; |
COEF(fr)[0] = 1; |
| DEG(fr) = dm + 1; |
DEG(fr) = dm + 1; |
| } |
} |
| |
|
| int minimain(mod,n,m,c) |
int minimain(int mod,int n,int m,int **c) |
| register int mod; |
|
| int n,m; |
|
| register int **c; |
|
| { |
{ |
| register int *ptr,*ci,*p; |
register int *ptr,*ci,*p; |
| register int i,l,a,j,b,inv; |
register int i,l,a,j,b,inv; |
| int *tmp; |
int *tmp; |
| |
|
| for ( j = 0; j < m; j++ ) { |
for ( j = 0; j < m; j++ ) { |
| for ( i = j; (n > i) && !c[i][j]; i++ ); |
for ( i = j; (n > i) && !c[i][j]; i++ ); |
| if ( i == n ) { |
if ( i == n ) { |
| for ( i = j, j = j - 1; j >= 0; j-- ) |
for ( i = j, j = j - 1; j >= 0; j-- ) |
| c[0][j] = c[j][i]; |
c[0][j] = c[j][i]; |
| c[0][i] = mod - 1; |
c[0][i] = mod - 1; |
| return( i ); |
return( i ); |
| } |
} |
| if ( i != j ) { |
if ( i != j ) { |
| tmp = c[i]; c[i] = c[j]; c[j] = tmp; |
tmp = c[i]; c[i] = c[j]; c[j] = tmp; |
| } |
} |
| ptr = c[j]; inv = invm((ptr[j] + mod) % mod,mod); |
ptr = c[j]; inv = invm((ptr[j] + mod) % mod,mod); |
| for ( l = j, p = ptr+l; l < m; l++ ) { |
for ( l = j, p = ptr+l; l < m; l++ ) { |
| a = (*p * inv) % mod; |
a = (*p * inv) % mod; |
| *p++ = (a<0?a+mod:a); |
*p++ = (a<0?a+mod:a); |
| } |
} |
| for ( i = 0; i < n; i++ ) |
for ( i = 0; i < n; i++ ) |
| if ( (a = -c[i][j]) && (i != j) ) { |
if ( (a = -c[i][j]) && (i != j) ) { |
| for ( l = j+1, p = ptr+l, ci = c[i]+l; l < m; l++ ) { |
for ( l = j+1, p = ptr+l, ci = c[i]+l; l < m; l++ ) { |
| b = (*p++ * a + *ci) % mod; |
b = (*p++ * a + *ci) % mod; |
| *ci++ = (b<0?b+mod:b); |
*ci++ = (b<0?b+mod:b); |
| } |
} |
| c[i][j] = 0; |
c[i][j] = 0; |
| } |
} |
| } |
} |
| return (-1); |
return (-1); |
| } |
} |
| |
|
| #if defined(__GNUC__) |
#if defined(__GNUC__) |
| const |
const |
| #endif |
#endif |
| int sprime[] = { |
int sprime[] = { |
| 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47, |
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47, |
| 53,59,61,67,71,73,79,83,89,97,101,103,107,109,113, |
53,59,61,67,71,73,79,83,89,97,101,103,107,109,113, |
| 127,131,137,139,149,151,157,163,167,173,179,181,191,193,197, |
127,131,137,139,149,151,157,163,167,173,179,181,191,193,197, |
| 199,211,223,227,229,233,239,241,251,257,263,269,271,277,281, |
199,211,223,227,229,233,239,241,251,257,263,269,271,277,281, |
| 283,293,307,311,313,317,331,337,347,349,353,359,367,373,379, |
283,293,307,311,313,317,331,337,347,349,353,359,367,373,379, |
| 383,389,397,401,409,419,421,431,433,439,443,449,457,461,463, |
383,389,397,401,409,419,421,431,433,439,443,449,457,461,463, |
| 467,479,487,491,499,503,509,521,523,541,547,557,563,569,571, |
467,479,487,491,499,503,509,521,523,541,547,557,563,569,571, |
| 577,587,593,599,601,607,613,617,619,631,641,643,647,653,659, |
577,587,593,599,601,607,613,617,619,631,641,643,647,653,659, |
| 661,673,677,683,691,701,709,719,727,733,739,743,751,757,761, |
661,673,677,683,691,701,709,719,727,733,739,743,751,757,761, |
| 769,773,787,797,809,811,821,823,827,829,839,853,857,859,863, |
769,773,787,797,809,811,821,823,827,829,839,853,857,859,863, |
| 877,881,883,887,907,911,919,929,937,941,947,953,967,971,977, |
877,881,883,887,907,911,919,929,937,941,947,953,967,971,977, |
| 983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069, |
983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069, |
| 1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187, |
1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187, |
| 1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291, |
1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291, |
| 1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427, |
1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427, |
| 1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511, |
1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511, |
| 1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613, |
1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613, |
| 1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733, |
1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733, |
| 1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867, |
1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867, |
| 1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987, |
1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987, |
| 1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087, |
1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087, |
| 2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213, |
2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213, |
| 2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333, |
2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333, |
| 2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423, |
2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423, |
| 2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557, |
2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557, |
| 2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687, |
2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687, |
| 2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789, |
2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789, |
| 2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903, |
2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903, |
| 2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037, |
2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037, |
| 3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181, |
3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181, |
| 3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307, |
3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307, |
| 3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413, |
3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413, |
| 3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539, |
3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539, |
| 3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643, |
3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643, |
| 3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769, |
3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769, |
| 3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907, |
3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907, |
| 3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019, |
3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019, |
| 4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139, |
4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139, |
| 4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261, |
4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261, |
| 4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409, |
4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409, |
| 4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523, |
4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523, |
| 4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657, |
4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657, |
| 4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793, |
4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793, |
| 4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937, |
4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937, |
| 4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039, |
4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039, |
| 5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179, |
5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179, |
| 5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323, |
5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323, |
| 5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443, |
5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443, |
| 5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569, |
5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569, |
| 5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693, |
5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693, |
| 5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827, |
5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827, |
| 5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939, |
5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939, |
| 5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091, |
5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091, |
| 6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221, |
6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221, |
| 6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337, |
6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337, |
| 6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473, |
6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473, |
| 6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619, |
6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619, |
| 6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761, |
6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761, |
| 6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871, |
6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871, |
| 6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997, |
6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997, |
| 7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151, |
7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151, |
| 7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297, |
7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297, |
| 7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459, |
7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459, |
| 7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561, |
7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561, |
| 7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687, |
7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687, |
| 7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829, |
7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829, |
| 7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951, |
7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951, |
| 7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111, |
7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111, |
| 8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243, |
8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243, |
| 8263,8269,8273,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387, |
8263,8269,8273,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387, |
| 8389,8419,8423,8429,8431,8443,8447,8461,8467,8501,8513,8521,8527,8537,8539, |
8389,8419,8423,8429,8431,8443,8447,8461,8467,8501,8513,8521,8527,8537,8539, |
| 8543,8563,8573,8581,8597,8599,8609,8623,8627,8629,8641,8647,8663,8669,8677, |
8543,8563,8573,8581,8597,8599,8609,8623,8627,8629,8641,8647,8663,8669,8677, |
| 8681,8689,8693,8699,8707,8713,8719,8731,8737,8741,8747,8753,8761,8779,8783, |
8681,8689,8693,8699,8707,8713,8719,8731,8737,8741,8747,8753,8761,8779,8783, |
| 8803,8807,8819,8821,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923,8929, |
8803,8807,8819,8821,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923,8929, |
| 8933,8941,8951,8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049, |
8933,8941,8951,8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049, |
| 9059,9067,9091,9103,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187,9199, |
9059,9067,9091,9103,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187,9199, |
| 9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337, |
9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337, |
| 9341,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439, |
9341,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439, |
| 9461,9463,9467,9473,9479,9491,9497,9511,9521,9533,9539,9547,9551,9587,9601, |
9461,9463,9467,9473,9479,9491,9497,9511,9521,9533,9539,9547,9551,9587,9601, |
| 9613,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721,9733, |
9613,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721,9733, |
| 9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851, |
9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851, |
| 9857,9859,9871,9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973,10007, |
9857,9859,9871,9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973,10007, |
| 10009,10037,10039,10061,10067,10069,10079,10091,10093,10099, |
10009,10037,10039,10061,10067,10069,10079,10091,10093,10099, |
| 10103,10111,10133,10139,10141,10151,10159,10163,10169,10177, |
10103,10111,10133,10139,10141,10151,10159,10163,10169,10177, |
| 10181,10193,10211,10223,10243,10247,10253,10259,10267,10271, |
10181,10193,10211,10223,10243,10247,10253,10259,10267,10271, |
| 10273,10289,10301,10303,10313,10321,10331,10333,10337,10343, |
10273,10289,10301,10303,10313,10321,10331,10333,10337,10343, |
| 10357,10369,10391,10399,10427,10429,10433,10453,10457,10459, |
10357,10369,10391,10399,10427,10429,10433,10453,10457,10459, |
| 10463,10477,10487,10499,10501,10513,10529,10531,10559,10567, |
10463,10477,10487,10499,10501,10513,10529,10531,10559,10567, |
| 10589,10597,10601,10607,10613,10627,10631,10639,10651,10657, |
10589,10597,10601,10607,10613,10627,10631,10639,10651,10657, |
| 10663,10667,10687,10691,10709,10711,10723,10729,10733,10739, |
10663,10667,10687,10691,10709,10711,10723,10729,10733,10739, |
| 10753,10771,10781,10789,10799,10831,10837,10847,10853,10859, |
10753,10771,10781,10789,10799,10831,10837,10847,10853,10859, |
| 10861,10867,10883,10889,10891,10903,10909,10937,10939,10949, |
10861,10867,10883,10889,10891,10903,10909,10937,10939,10949, |
| 10957,10973,10979,10987,10993,11003,11027,11047,11057,11059, |
10957,10973,10979,10987,10993,11003,11027,11047,11057,11059, |
| 11069,11071,11083,11087,11093,11113,11117,11119,11131,11149, |
11069,11071,11083,11087,11093,11113,11117,11119,11131,11149, |
| 11159,11161,11171,11173,11177,11197,11213,11239,11243,11251, |
11159,11161,11171,11173,11177,11197,11213,11239,11243,11251, |
| 11257,11261,11273,11279,11287,11299,11311,11317,11321,11329, |
11257,11261,11273,11279,11287,11299,11311,11317,11321,11329, |
| 11351,11353,11369,11383,11393,11399,11411,11423,11437,11443, |
11351,11353,11369,11383,11393,11399,11411,11423,11437,11443, |
| 11447,11467,11471,11483,11489,11491,11497,11503,11519,11527, |
11447,11467,11471,11483,11489,11491,11497,11503,11519,11527, |
| 11549,11551,11579,11587,11593,11597,11617,11621,11633,11657, |
11549,11551,11579,11587,11593,11597,11617,11621,11633,11657, |
| 11677,11681,11689,11699,11701,11717,11719,11731,11743,11777, |
11677,11681,11689,11699,11701,11717,11719,11731,11743,11777, |
| 11779,11783,11789,11801,11807,11813,11821,11827,11831,11833, |
11779,11783,11789,11801,11807,11813,11821,11827,11831,11833, |
| 11839,11863,11867,11887,11897,11903,11909,11923,11927,11933, |
11839,11863,11867,11887,11897,11903,11909,11923,11927,11933, |
| 11939,11941,11953,11959,11969,11971,11981,11987,12007,12011, |
11939,11941,11953,11959,11969,11971,11981,11987,12007,12011, |
| 12037,12041,12043,12049,12071,12073,12097,12101,12107,12109, |
12037,12041,12043,12049,12071,12073,12097,12101,12107,12109, |
| 12113,12119,12143,12149,12157,12161,12163,12197,12203,12211, |
12113,12119,12143,12149,12157,12161,12163,12197,12203,12211, |
| 12227,12239,12241,12251,12253,12263,12269,12277,12281,12289, |
12227,12239,12241,12251,12253,12263,12269,12277,12281,12289, |
| 12301,12323,12329,12343,12347,12373,12377,12379,12391,12401, |
12301,12323,12329,12343,12347,12373,12377,12379,12391,12401, |
| 12409,12413,12421,12433,12437,12451,12457,12473,12479,12487, |
12409,12413,12421,12433,12437,12451,12457,12473,12479,12487, |
| 12491,12497,12503,12511,12517,12527,12539,12541,12547,12553, |
12491,12497,12503,12511,12517,12527,12539,12541,12547,12553, |
| 12569,12577,12583,12589,12601,12611,12613,12619,12637,12641, |
12569,12577,12583,12589,12601,12611,12613,12619,12637,12641, |
| 12647,12653,12659,12671,12689,12697,12703,12713,12721,12739, |
12647,12653,12659,12671,12689,12697,12703,12713,12721,12739, |
| 12743,12757,12763,12781,12791,12799,12809,12821,12823,12829, |
12743,12757,12763,12781,12791,12799,12809,12821,12823,12829, |
| 12841,12853,12889,12893,12899,12907,12911,12917,12919,12923, |
12841,12853,12889,12893,12899,12907,12911,12917,12919,12923, |
| 12941,12953,12959,12967,12973,12979,12983,13001,13003,13007, |
12941,12953,12959,12967,12973,12979,12983,13001,13003,13007, |
| 13009,13033,13037,13043,13049,13063,13093,13099,13103,13109, |
13009,13033,13037,13043,13049,13063,13093,13099,13103,13109, |
| 13121,13127,13147,13151,13159,13163,13171,13177,13183,13187, |
13121,13127,13147,13151,13159,13163,13171,13177,13183,13187, |
| 13217,13219,13229,13241,13249,13259,13267,13291,13297,13309, |
13217,13219,13229,13241,13249,13259,13267,13291,13297,13309, |
| 13313,13327,13331,13337,13339,13367,13381,13397,13399,13411, |
13313,13327,13331,13337,13339,13367,13381,13397,13399,13411, |
| 13417,13421,13441,13451,13457,13463,13469,13477,13487,13499, |
13417,13421,13441,13451,13457,13463,13469,13477,13487,13499, |
| 13513,13523,13537,13553,13567,13577,13591,13597,13613,13619, |
13513,13523,13537,13553,13567,13577,13591,13597,13613,13619, |
| 13627,13633,13649,13669,13679,13681,13687,13691,13693,13697, |
13627,13633,13649,13669,13679,13681,13687,13691,13693,13697, |
| 13709,13711,13721,13723,13729,13751,13757,13759,13763,13781, |
13709,13711,13721,13723,13729,13751,13757,13759,13763,13781, |
| 13789,13799,13807,13829,13831,13841,13859,13873,13877,13879, |
13789,13799,13807,13829,13831,13841,13859,13873,13877,13879, |
| 13883,13901,13903,13907,13913,13921,13931,13933,13963,13967, |
13883,13901,13903,13907,13913,13921,13931,13933,13963,13967, |
| 13997,13999,14009,14011,14029,14033,14051,14057,14071,14081, |
13997,13999,14009,14011,14029,14033,14051,14057,14071,14081, |
| 14083,14087,14107,14143,14149,14153,14159,14173,14177,14197, |
14083,14087,14107,14143,14149,14153,14159,14173,14177,14197, |
| 14207,14221,14243,14249,14251,14281,14293,14303,14321,14323, |
14207,14221,14243,14249,14251,14281,14293,14303,14321,14323, |
| 14327,14341,14347,14369,14387,14389,14401,14407,14411,14419, |
14327,14341,14347,14369,14387,14389,14401,14407,14411,14419, |
| 14423,14431,14437,14447,14449,14461,14479,14489,14503,14519, |
14423,14431,14437,14447,14449,14461,14479,14489,14503,14519, |
| 14533,14537,14543,14549,14551,14557,14561,14563,14591,14593, |
14533,14537,14543,14549,14551,14557,14561,14563,14591,14593, |
| 14621,14627,14629,14633,14639,14653,14657,14669,14683,14699, |
14621,14627,14629,14633,14639,14653,14657,14669,14683,14699, |
| 14713,14717,14723,14731,14737,14741,14747,14753,14759,14767, |
14713,14717,14723,14731,14737,14741,14747,14753,14759,14767, |
| 14771,14779,14783,14797,14813,14821,14827,14831,14843,14851, |
14771,14779,14783,14797,14813,14821,14827,14831,14843,14851, |
| 14867,14869,14879,14887,14891,14897,14923,14929,14939,14947, |
14867,14869,14879,14887,14891,14897,14923,14929,14939,14947, |
| 14951,14957,14969,14983,15013,15017,15031,15053,15061,15073, |
14951,14957,14969,14983,15013,15017,15031,15053,15061,15073, |
| 15077,15083,15091,15101,15107,15121,15131,15137,15139,15149, |
15077,15083,15091,15101,15107,15121,15131,15137,15139,15149, |
| 15161,15173,15187,15193,15199,15217,15227,15233,15241,15259, |
15161,15173,15187,15193,15199,15217,15227,15233,15241,15259, |
| 15263,15269,15271,15277,15287,15289,15299,15307,15313,15319, |
15263,15269,15271,15277,15287,15289,15299,15307,15313,15319, |
| 15329,15331,15349,15359,15361,15373,15377,15383,15391,15401, |
15329,15331,15349,15359,15361,15373,15377,15383,15391,15401, |
| 15413,15427,15439,15443,15451,15461,15467,15473,15493,15497, |
15413,15427,15439,15443,15451,15461,15467,15473,15493,15497, |
| 15511,15527,15541,15551,15559,15569,15581,15583,15601,15607, |
15511,15527,15541,15551,15559,15569,15581,15583,15601,15607, |
| 15619,15629,15641,15643,15647,15649,15661,15667,15671,15679, |
15619,15629,15641,15643,15647,15649,15661,15667,15671,15679, |
| 15683,15727,15731,15733,15737,15739,15749,15761,15767,15773, |
15683,15727,15731,15733,15737,15739,15749,15761,15767,15773, |
| 15787,15791,15797,15803,15809,15817,15823,15859,15877,15881, |
15787,15791,15797,15803,15809,15817,15823,15859,15877,15881, |
| 15887,15889,15901,15907,15913,15919,15923,15937,15959,15971, |
15887,15889,15901,15907,15913,15919,15923,15937,15959,15971, |
| 15973,15991,16001,16007,16033,16057,16061,16063,16067,16069, |
15973,15991,16001,16007,16033,16057,16061,16063,16067,16069, |
| 16073,16087,16091,16097,16103,16111,16127,16139,16141,16183, |
16073,16087,16091,16097,16103,16111,16127,16139,16141,16183, |
| 16187,16189,16193,16217,16223,16229,16231,16249,16253,16267, |
16187,16189,16193,16217,16223,16229,16231,16249,16253,16267, |
| 16273,16301,16319,16333,16339,16349,16361,16363,16369,16381, |
16273,16301,16319,16333,16339,16349,16361,16363,16369,16381, |
| 0 |
0 |
| }; |
}; |
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