Lucas定理

Code(luogu P3807):

#include<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long 
#define MN 100005
using namespace std;
inline int in(){
    int x=0;bool f=0; char c;
    for (;(c=getchar())<'0'||c>'9';f=c=='-');
    for (x=c-'0';(c=getchar())>='0'&&c<='9';x=(x<<3)+(x<<1)+c-'0');
    return f?-x:x;
}
ll fct[MN];
int n,m,p,T;
inline int qpow(ll x,int k){
    ll res=1ll;while (k){
        if (k&1) res=(res*x)%p;
        x=(x*x)%p;k>>=1;
    }return res;
}
inline ll calc(ll x,ll y){
    return (x<y)?0ll:(fct[x]*qpow(fct[y],p-2)%p*qpow(fct[x-y],p-2))%p;
} 
inline ll lucas(ll x,ll y){
    return (y)?(calc(x%p,y%p)*lucas(x/p,y/p))%p:1ll;
}
int main()
{
    T=in();while (T--){
        n=in();m=in();p=in();fct[0]=1ll;
        for (int i=1;i<=n+m;++i) fct[i]=(1ll*fct[i-1]*i)%p;
        printf("%d\n",lucas(n+m,n)%p);
    }return 0;
}