Avito Cool Challenge 2018 C. Colorful Bricks 组合数学

C. Colorful Bricks

input

4 2 3

output

2

code

//Siberian Squirrel
#include<bits/stdc++.h>

#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define ACM_LOCAL

using namespace std;
typedef long long ll;

const int N = 2e5 + 10;
const int MOD = 998244353;

ll n, m, k;
int f[N];

ll quick_pow(ll ans, ll p, ll res = 1) {
    
    
    for(; p; p >>= 1, ans = ans * ans % MOD)
        if(p & 1) res = res * ans % MOD;
    return res % MOD;
}

ll inv(ll ans) {
    
    
    return quick_pow(ans, MOD - 2);
}

ll C(int n, int m) {
    
    
    if(n < m || n <= 0 || m < 0) return 0;
    if(m == 0) return 1;
    return 1ll * f[n] * inv(f[m]) % MOD * inv(f[n - m]) % MOD;
}

inline void solve(ll res = 0, ll ans = 1) {
    
    
    if(!k)
        res = m;
    else
        res = C(n - 1, k) * m % MOD * quick_pow(m - 1, k) % MOD;
    cout << res << endl;
}

int main() {
    
    
    IO;
#ifdef ACM_LOCAL
    freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
#endif
	f[0] = f[1] = 1;
	for(int i = 2; i < N; ++ i) f[i] = 1ll * f[i - 1] * i % MOD;
    int o = 1;
//    cin >> o;
    while(o --) {
    
    
        cin >> n >> m >> k;
        solve();
    }

    return 0;
}