countings.h

class Countings{
    private:
        int mod;
        vector<long long> factList, invList;
        long long Pow(long long x, long long n);
    public:
        Countings(int sz, int mod);
        long long Permutation(int n, int r);
        long long Combination(int n, int r);
        long long HomogeneousProduct(int n, int r);
};

Countings::Countings(int sz, int mod) : mod(mod), factList(sz + 1), invList(sz + 1) {
    factList[0] = 1;
    for(int i = 1; i < factList.size(); i++) {
        factList[i] = factList[i - 1] * i % mod;
    }
    invList[sz] = Pow(factList[sz], mod - 2);
    for(int i = sz - 1; i >= 0; i--) {
        invList[i] = invList[i + 1] * (i + 1) % mod;
    }
}

long long Countings::Pow(long long x, long long n){
    long long ret = 1;
    while(n > 0) {
      if(n & 1) ret = ret * x % mod;
      x = x * x % mod;
      n >>= 1;
    }
    return ret;
}

long long Countings::Permutation(int n, int r){
    if(r < 0 || n < r) return 0;
    return factList[n] * invList[n - r] % mod;
}

long long Countings::Combination(int n, int r){
    if(r < 0 || n < r) return 0;
    return factList[n] * invList[r] % mod * invList[n - r] % mod;
}

long long Countings::HomogeneousProduct(int n, int r){
    if(n < 0 || r < 0) return 0;
    return (r == 0 ? 1 : Combination(n + r - 1, r));
}