题解

#include <bits/stdc++.h>//万能头
using namespace std;
typedef long long ll;
const int MOD = 998244353;
const int N = 105,M = 2005;
int n, m;
ll a[N][M], s[N];
ll dp[2][2 * N + 5];
int main(){//主函数
    ios::sync_with_stdio(false);
    cin.tie(nullptr);//对cin和cout加速
    cin >> n >> m;
    for(int i = 1;i <= n;i++){
        s[i] = 0;
        for(int j = 1;j <= m;j++){
            cin >> a[i][j];
            s[i] = (s[i] + a[i][j]) % MOD;
        }
    }
    ll total = 1;
    for(int i = 1;i <= n;i++){
        total = total * (s[i] + 1) % MOD;
    }
    total = (total - 1 + MOD) % MOD;
    ll invalid = 0;
    const int offset = N;
    for(int j = 1;j <= m;j++){
        memset(dp, 0, sizeof(dp));
        int cur = 0;
        dp[cur][offset] = 1;
        for(int i = 1;i <= n;i++){
            int prev = cur;
            cur ^= 1;
            memset(dp[cur],0,sizeof(dp[cur]));
            ll c1 = a[i][j] % MOD;
            ll c2 = (s[i] - c1 + MOD) % MOD;
            for(int d_prev = 0;d_prev <= 2 * N;d_prev++){
                if (dp[prev][d_prev] == 0) continue;
                dp[cur][d_prev] = (dp[cur][d_prev] + dp[prev][d_prev]) % MOD;
                int d_new = d_prev + 1;
                if(d_new <= 2 * N){
                    dp[cur][d_new] = (dp[cur][d_new] + dp[prev][d_prev] * c1) % MOD;
                }
                d_new = d_prev - 1;
                if(d_new >= 0 && d_new <= 2 * N){
                    dp[cur][d_new] = (dp[cur][d_new] + dp[prev][d_prev] * c2) % MOD;
                }
            }
        }
        for(int d = offset + 1;d <= 2 * N;d++){
            invalid = (invalid + dp[cur][d]) % MOD;
        }
    }
    ll ans = (total - invalid + MOD) % MOD;
    cout << ans;
    return 0;
}