modint.cpp

//
// modint
//
// reference:
//   drken: 「1000000007 で割ったあまり」の求め方を総特集！ ～ 逆元から離散対数まで ～
//     https://qiita.com/drken/items/3b4fdf0a78e7a138cd9a
//
// verified:
//   ABC 127 E - Cell Distance
//     https://atcoder.jp/contests/abc127/tasks/abc127_e
//


#include <bits/stdc++.h>
using namespace std;


// modint
template<int MOD> struct Fp {
    // inner value
    long long val;
    
    // constructor
    constexpr Fp() : val(0) { }
    constexpr Fp(long long v) : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    
    // getter
    constexpr long long get() const {
        return val;
    }
    constexpr int get_mod() const {
        return MOD;
    }
    
    // comparison operators
    constexpr bool operator == (const Fp &r) const {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp &r) const {
        return this->val != r.val;
    }
    
    // arithmetic operators
    constexpr Fp& operator += (const Fp &r) {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp &r) {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp &r) {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp &r) {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b, swap(a, b);
            u -= t * v, swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp operator + () const { return Fp(*this); }
    constexpr Fp operator - () const { return Fp(0) - Fp(*this); }
    constexpr Fp operator + (const Fp &r) const { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp &r) const { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp &r) const { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp &r) const { return Fp(*this) /= r; }
    
    // other operators
    constexpr Fp& operator ++ () {
        ++val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -- () {
        if (val == 0) val += MOD;
        --val;
        return *this;
    }
    constexpr Fp operator ++ (int) {
        Fp res = *this;
        ++*this;
        return res;
    }
    constexpr Fp operator -- (int) {
        Fp res = *this;
        --*this;
        return res;
    }
    friend constexpr istream& operator >> (istream &is, Fp<MOD> &x) {
        is >> x.val;
        x.val %= MOD;
        if (x.val < 0) x.val += MOD;
        return is;
    }
    friend constexpr ostream& operator << (ostream &os, const Fp<MOD> &x) {
        return os << x.val;
    }
    
    // other functions
    constexpr Fp pow(long long n) const {
        Fp res(1), mul(*this);
        while (n > 0) {
            if (n & 1) res *= mul;
            mul *= mul;
            n >>= 1;
        }
        return res;
    }
    constexpr Fp inv() const {
        Fp res(1), div(*this);
        return res / div;
    }
    friend constexpr Fp<MOD> pow(const Fp<MOD> &r, long long n) {
        return r.pow(n);
    }
    friend constexpr Fp<MOD> inv(const Fp<MOD> &r) {
        return r.inv();
    }
};

// Binomial coefficient
template<class mint> struct BiCoef {
    vector<mint> fact_, inv_, finv_;
    constexpr BiCoef() {}
    constexpr BiCoef(int n) : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
        init(n);
    }
    constexpr void init(int n) {
        fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
        int MOD = fact_[0].get_mod();
        for(int i = 2; i < n; i++){
            fact_[i] = fact_[i-1] * i;
            inv_[i] = -inv_[MOD%i] * (MOD/i);
            finv_[i] = finv_[i-1] * inv_[i];
        }
    }
    constexpr mint com(int n, int k) const {
        if (n < k || n < 0 || k < 0) return 0;
        return fact_[n] * finv_[k] * finv_[n-k];
    }
    constexpr mint fact(int n) const {
        if (n < 0) return 0;
        return fact_[n];
    }
    constexpr mint inv(int n) const {
        if (n < 0) return 0;
        return inv_[n];
    }
    constexpr mint finv(int n) const {
        if (n < 0) return 0;
        return finv_[n];
    }
};



//------------------------------//
// Examples
//------------------------------//

void small_test() {
    const int MOD = 998244353;
    using mint = Fp<MOD>;
    
    auto check = [&](mint val, mint res) -> void {
        cout << val << endl;
        assert(val == res);
    };
    
    // arithmetic operation
    mint a = -3;
    mint b = 5;
    check(a + b, 2);
    check(a - b, 998244345);  // -8
    check(a * b, 998244338);  // -15
    a += b;
    check(a, 2);
    a -= 3;
    check(a, 998244352);  // -1
    a *= 6;
    check(a, 998244347);  // -6
    a /= 2;
    check(a, 998244350);  // -3

    // increment
    check(++a, 998244351);  // -2
    check(a, 998244351);  // -2
    check(--a, 998244350);  // -3
    check(a, 998244350);  // -3
    check(b++, 5);
    check(b, 6);
    check(b--, 6);
    check(b, 5);
    
    // division
    a = 6, b = 2;
    check(a / b, 3);
    mint c = b / a;
    check(c, 332748118);
    check(c * a, 2);
    
    // pow, inv
    check(b.pow(20), 1048576);
    check(b.inv(), 499122177);
}

void ABC_127_E() {
    const int MOD = 1000000007;
    using mint = Fp<MOD>;

    long long N, M, K;
    cin >> N >> M >> K;
    
    BiCoef<mint> bc(N * M);
    mint sum = 0;
    for (int i = 0; i <= N-1; ++i) {
        for (int j = 0; j <= M-1; ++j) {
            mint tmp = mint(N - i) * mint(M - j) * mint(i + j);
            if (i != 0 && j != 0) tmp *= 2;
            sum += tmp;
        }
    }
    cout << sum * bc.com(N * M - 2, K - 2) << endl;
}


int main() {
    small_test();
    //ABC_127_E();
}