LUCAS（数论定理）

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#include<iostream>
#include<algorithm>
#include<cstdio>
using namespace std;
typedef long long LL;
using namespace std;

LL exp_mod(LL a, LL b, LL p) {
    LL res = 1;
    while(b != 0) {
        if(b&1) res = (res * a) % p;
        a = (a*a) % p;
        b >>= 1;
    }
    return res;
}

LL Comb(LL a, LL b, LL p) {
    if(a < b)   return 0;
    if(a == b)  return 1;
    if(b > a - b)   b = a - b;

    LL ans = 1, ca = 1, cb = 1;
    for(LL i = 0; i < b; ++i) {
        ca = (ca * (a - i))%p;
        cb = (cb * (b - i))%p;
    }
    ans = (ca*exp_mod(cb, p - 2, p)) % p;
    return ans;
}

LL Lucas(int n, int m, int p) {
     LL ans = 1;

     while(n&&m&&ans) {
        ans = (ans*Comb(n%p, m%p, p)) % p;
        n /= p;
        m /= p;
     }
     return ans;
}

int main() {
    //Read();
    int n, m, p;
    while(~scanf("%d%d%d", &n, &m, &p)) {
        printf("%lld\n", Lucas(n, m, p));
    }
    return 0;
}