【数论】Lucas定理

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#define ll long long int
using namespace std;
ll t,p;
ll ksm(ll a,ll b){
    ll tot=1;
    while(b){
        if(b&1){
        tot=(tot*a)%p;    
        }
        a=(a*a)%p;
        b>>=1;
    }
    return tot;
}
ll c(ll n,ll m){
    if(m>n)return 0;
    ll t1=1,t2=1;
    for(register int i=n-m+1;i<=n;i++)t1=(t1*i)%p;
    for(register int i=1;i<=m;i++)t2=(t2*i)%p;
    return t1*ksm(t2,p-2)%p;
}
ll lucas(ll n,ll m){
    if(!m)return 1;
    else
    return (lucas(n/p,m/p)*c(n%p,m%p))%p;
}
int main(){
    scanf("%lld",&t);
    while(t){
    t--;
    ll n,m;
    scanf("%lld%lld%lld",&n,&m,&p);
    printf("%lld\n",lucas(n+m,m));
    }
    return 0;
}