expectedvalue.cpp

// Ivan Carvalho
// Solution to https://dmoj.ca/problem/expectedvalue
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const int MAXN = 1e3 + 10;
const int MOD = 998244353;
const ll INVMOD[11] = {0,           1LL,         499122177LL, 332748118LL,
                       748683265LL, 598946612LL, 166374059LL, 855638017LL,
                       873463809LL, 443664157LL, 299473306LL};

ll dp[MAXN][MAXN][2], matriz[MAXN][MAXN], prob[2];
int N, A, B;

ll solve(int x, int y, int o) {
    if (dp[x][y][o] != -1) return dp[x][y][o];
    if (x == N && y == N) return dp[x][y][o] = matriz[x][y];
    int nx = x + (o == 1 ? 1 : 0);
    int ny = y + (o == 1 ? 0 : 1);
    if (nx > N || ny > N) return dp[x][y][o] = solve(x, y, o ^ 1);
    ll ans = prob[0] * solve(nx, ny, o) + prob[1] * solve(nx, ny, o ^ 1);
    return dp[x][y][o] = (matriz[x][y] + ans) % MOD;
}

int main() {
    scanf("%d %d", &A, &B);
    prob[0] = ((B - A) * INVMOD[B]) % MOD;
    prob[1] = (A * INVMOD[B]) % MOD;

    memset(dp, -1, sizeof(dp));
    scanf("%d", &N);
    for (int i = 1; i <= N; i++) {
        for (int j = 1; j <= N; j++) scanf("%lld", &matriz[i][j]);
    }

    ll ans = prob[0] * solve(1, 1, 1) + prob[1] * solve(1, 1, 0);
    printf("%lld\n", ans % MOD);

    return 0;
}