CF1278F Cards

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$\begin{aligned}
&\sum_{i=0}^n{n\choose i}p^i(1-p)^{n-i}i^k\\
=&\sum_{i=0}^n{n\choose i}p^i(1-p)^{n-i}\sum_{j=0}^k{i\choose j}j!\begin{Bmatrix}
k \\ j
\end{Bmatrix}\\
=&\sum_{j=0}^k\begin{Bmatrix}
k \\ j
\end{Bmatrix}j!\sum_{i=0}^n{n\choose i}{i\choose j}p^i(1-p)^{n-i}\\
=&\sum_{j=0}^k\begin{Bmatrix}
k \\ j
\end{Bmatrix}j!\sum_{i=0}^n{n\choose j}{n-j\choose i-j}p^i(1-p)^{n-i}\\
=&\sum_{j=0}^k\begin{Bmatrix}
k \\ j
\end{Bmatrix}n^{\underline j}p^j\sum_{i=0}^{n}{n-j\choose i-j}p^{i-j}(1-p)^{n-i}\\
=&\sum_{j=0}^k\begin{Bmatrix}
k \\ j
\end{Bmatrix}n^{\underline j}p^j
\end{aligned}$

?? 
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#include <iostream>
#include <cstdio>
#include <algorithm>
#include <queue>
#include <cmath>
#include <cstring>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 5e3 + 10;
const int mod = 998244353;
int s[N][N], Cn[N];
int k, m, n;
int qpow(int a, int b, int mo)
{
    int res = 1;
    while (b)
    {
        if (b & 1)
            res = 1ll * res * a % mo;
        a = 1ll * a * a % mo;
        b >>= 1;
    }
    return res;
}
void init()
{
    s[0][0] = 1;
    for (int i = 1; i <= k; i++)
    {
        for (int j = 1; j <= i; j++)
        {
            s[i][j] = (1ll * s[i - 1][j] * j % mod + s[i - 1][j - 1]) % mod;
        }
    }
    Cn[0] = 1;
    for (int i = 1; i <= k; i++)
        Cn[i] = 1ll * Cn[i - 1] * (n - i + 1) % mod;
}
int ans = 0;
int main()
{
    scanf("%d%d%d", &n, &m, &k);
    init();
    int p = qpow(m, mod - 2, mod);
    for (int i = 0; i <= k; i++)
    {
        ans = (ans + 1ll * s[k][i] * Cn[i] % mod * qpow(p, i, mod) % mod) % mod;
    }
    printf("%d\n", ans);
}