int main()
{
long long i,n,r,t,t1,t2,t3,t4,t5,crt;
int cases,A,B;
a[0][0]=1;a[0][1]=1;
a[1][0]=1;a[1][1]=1;
for(i=1;i<200007;i++){
a[i][0] = (i*a[i-1][0])%2;
// printf("%d\n",a[i][0]);
a[i][1] = (i*a[i-1][1])%500000003;
}
b_41[0][0]=1;b_41[0][1]=0;
b_148721[0][0]=1;b_148721[0][1]=0;
for(i=1;i<200007;i++){
t=i;
b_41[i][1]=b_41[i-1][1];
while(t%41 == 0){t=t/41;b_41[i][1]++;}
b_41[i][0] = (t*b_41[i-1][0])%1681;
b_148721[i][0]=(i*b_148721[i-1][0])%148721;
b_148721[i][1]=0;
}
// printf("\n");
scanf("%d",&cases);
while(cases--)
{
scanf("%d %d %lld",&A,&B,&n);
if(A==0 && B==0)
{
printf("1\n");
continue;
}
t3 = (a[2*n][0]*power(a[n][0],0,2))%2;
t3 = (t3*power(a[n][0],0,2))%2;
t4 = (b_41[2*n][0]*inverse2(b_41[n][0],1681))%1681;
t4 = (t4*inverse2(b_41[n][0],1681))%1681;
t4 = (t4*power(41,b_41[2*n][1]-2*b_41[n][1],1681))%1681;
// printf("%lld",t4);
// return 0;
t5 = (b_148721[2*n][0]*power(b_148721[n][0],148719,148721))%148721;
t5 = (t5*power(b_148721[n][0],148719,148721))%148721;
//printf("t3=%lld t4=%lld t5=%lld\n",t3,t4,t5);
crt = chinese_remainder_2(t3,t4,t5);
t2 = power(B,crt,500000003);
t1 = power(B,0,2);
//printf("crt1=%lld t1=%lld t2=%lld\n",crt,t1,t2);
// t2 = (a[2*n][1]*power(a[n][1],500000001,500000003))%500000003;
// t2 = (t2*power(a[n][1],500000001,500000003))%500000003;
// printf("%lld\n",t2);
crt = chinese_remainder(t1,t2);
//printf("A=%d crt = %d\n",A,crt);
printf("%lld\n",power(A,crt,1000000007));
}
return 0;
}
GF2m& GF2m::operator/=(const GF2m& b)
{
GF2m z=b;
inverse2(z.fn,z.fn);
modmult2(fn,z.fn,fn);
return *this;
}
GF2m operator/(const GF2m& b1,const GF2m& b2)
{
GF2m abb;
inverse2(b2.fn,abb.fn);
modmult2(b1.fn,abb.fn,abb.fn);
return abb;
}
int chinese_remainder_2(long long n1,long long n2,long long n3)
{
int p1=2,p2=1681,p3=148721;
long long m1,m2,m3;
long long i1,i2,i3;
long long m;
int ans;
m = p1*p2*p3;
m1 = m/p1;m2=m/p2;m3=m/p3;
i1 = inverse(m1,p1);i2=inverse2(m2,p2);i3=inverse(m3,p3);
//printf("i1 = %lld i2 = %lld\n",i1,i2);
ans = (n1*m1*i1)%m+(n2*m2*i2)%m + (n3*m3*i3)%m ;
ans = ans%m;
return ans;
//printf("%d\n",ans);
}
int main(int argc, char **argv)
{
double a = 1234.0;
double b;
double r2,r3,r4,r5;
b = 1.0 / a;
r2 = inverse2(a);
r3 = inverse3(a);
r4 = inverse4(a);
r5 = inverse5(a);
printf(" a = %5.16lf\n", a);
printf("true 1/a = %5.16lf\n", b);
printf(" r2 = %5.16lf\n", r2);
printf(" r3 = %5.16lf\n", r3);
printf(" r4 = %5.16lf\n", r4);
printf(" r5 = %5.16lf\n", r5);
return 0;
}
GF2m inverse(const GF2m& b) {
GF2m r=b;
inverse2(r.fn,r.fn);
return r;
}
void invert(_MIPD_ big *x)
{
int degF,degG,degB,degC,d,i,j;
big alpha,beta,gamma,BB[4],FF[5],CC[4],GG[5],t;
big *BP=BB,*CP=CC,*FP=FF,*GP=GG,*TP;
#ifndef MR_STATIC
char *mem=(char *)memalloc(_MIPP_ 22);
#else
char mem[MR_BIG_RESERVE(22)]; /* 972 bytes from the stack */
memset(mem,0,MR_BIG_RESERVE(22));
#endif
alpha=mirvar_mem(_MIPP_ mem,0);
beta=mirvar_mem(_MIPP_ mem,1);
gamma=mirvar_mem(_MIPP_ mem,2);
t=mirvar_mem(_MIPP_ mem,3);
for (i=0;i<4;i++)
BB[i]=mirvar_mem(_MIPP_ mem,4+i);
for (i=0;i<5;i++)
FF[i]=mirvar_mem(_MIPP_ mem,8+i);
for (i=0;i<4;i++)
CC[i]=mirvar_mem(_MIPP_ mem,13+i);
for (i=0;i<5;i++)
GG[i]=mirvar_mem(_MIPP_ mem,17+i);
convert(_MIPP_ 1,CP[0]);
convert(_MIPP_ 1,FP[0]);
convert(_MIPP_ 1,FP[1]);
convert(_MIPP_ 1,FP[4]); /* F = x^4+x+1 - irreducible polynomial for GF(2^{4m}) */
degF=4; degG=degree(x); degC=0; degB=-1;
if (degG==0)
{
inverse2(_MIPP_ x[0],x[0]);
return;
}
for (i=0;i<4;i++)
{
fcopy2(x[i],GP[i]);
zero(x[i]);
}
while (degF!=0)
{
if (degF<degG)
{ /* swap */
TP=FP; FP=GP; GP=TP; d=degF; degF=degG; degG=d;
TP=BP; BP=CP; CP=TP; d=degB; degB=degC; degC=d;
}
j=degF-degG;
modsquare2(_MIPP_ GP[degG],alpha);
modmult2(_MIPP_ FP[degF],GP[degG],beta);
modmult2(_MIPP_ GP[degG],FP[degF-1],t);
modmult2(_MIPP_ FP[degF],GP[degG-1],gamma);
fincr2(t,gamma);
zero(t);
for (i=0;i<=degF;i++ )
{
modmult2(_MIPP_ FP[i],alpha,FP[i]);
if (i>=j-1)
{
modmult2(_MIPP_ gamma,GP[i-j+1],t);
fincr2(t,FP[i]);
}
if (i>=j)
{
modmult2(_MIPP_ beta,GP[i-j],t);
fincr2(t,FP[i]);
}
}
for (i=0;i<=degB || i<=(degC+j);i++)
{
modmult2(_MIPP_ BP[i],alpha,BP[i]);
if (i>=j-1)
{
modmult2(_MIPP_ gamma,CP[i-j+1],t);
fincr2(t,BP[i]);
}
if (i>=j)
{
modmult2(_MIPP_ beta,CP[i-j],t);
fincr2(t,BP[i]);
}
}
while (degF>=0 && size(FP[degF])==0) degF--;
if (degF==degG)
{
fcopy2(FP[degF],alpha);
for (i=0;i<=degF;i++)
{
modmult2(_MIPP_ FP[i],GP[degF],FP[i]);
modmult2(_MIPP_ alpha,GP[i],t);
fincr2(t,FP[i]);
}
for (i=0;i<=4-degF;i++)
{
modmult2(_MIPP_ BP[i],GP[degF],BP[i]);
modmult2(_MIPP_ CP[i],alpha,t);
fincr2(t,BP[i]);
}
while (degF>=0 && size(FP[degF])==0) degF--;
}
degB=3;
while (degB>=0 && size(BP[degB])==0) degB--;
}
inverse2(_MIPP_ FP[0],alpha);
for (i=0;i<=degB;i++)
modmult2(_MIPP_ alpha,BP[i],x[i]);
#ifndef MR_STATIC
memkill(_MIPP_ mem,22);
#else
memset(mem,0,MR_BIG_RESERVE(22));
#endif
}
