洛谷.3807.[模板]卢卡斯定理(Lucas)

//想错int范围了...不要被longlong坑
//这个范围现算阶乘比预处理快得多
#include <cstdio>
typedef long long LL;
const int N=1e5+5;

LL n,m,p;//,fac[N+3];

LL FP(LL x,LL k,LL p)
{
LL t=1;
for(; k; k>>=1,x=x*x%p)
if(k&1) t=t*x%p;
return t;
}
inline LL inv(LL x,LL p)
{
return FP(x,p-2,p);
}
//LL C(LL n,LL m)
//{
//  if(n<m) return 0ll;
//  return fac
*inv(fac[m],p)%p*inv(fac[n-m],p)%p;
//}
LL C(LL n,LL m)
{
if(n<m) return 0ll;
LL up=1ll,down=1ll;
for(LL i=n-m+1; i<=n; ++i) (up*=i)%=p;
for(LL i=2; i<=m; ++i) (down*=i)%=p;
return up*inv(down,p)%p;
}
LL Lucas(LL n,LL m,LL p)
{
LL ans=1;
for(; m && ans; n/=p, m/=p)
(ans*=C(n%p,m%p))%=p;
return ans;
}

int main()
{
//  fac[0]=fac[1]=1;
LL t; scanf("%lld",&t);
while(t--)
{
scanf("%lld%lld%lld",&n,&m,&p);
//      for(LL i=2; i<=p; ++i) fac[i]=i*fac[i-1]%p;
printf("%lld\n",Lucas(n+m,m,p));
}
return 0;
}