Мышка и зернышки

#include <bits/stdc++.h>

using namespace std;

const int N = 105;

int n, m;
int a[N][N], dp[N][N];

int main(){
    cin >> n >> m;

    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            cin >> a[i][j];
        }
    }

    dp[n][1] = a[n][1];

    for (int i = n; i >= 1; i--) {
        for (int j = 1; j <= m; j++) {
            if (i == n && j == 1) continue;
            int first_value = 0, second_value = 0;
            if (i + 1 <= n) {
                first_value = dp[i + 1][j];
            }
            if (j - 1 >= 1) {
                second_value = dp[i][j - 1];
            }
            dp[i][j] = max(first_value, second_value) + a[i][j];
        }
    }

    string path;
    int x = 1, y = m;

    while (x != n || y != 1) {
//        cout << x << " " << y << endl;
        int first_value = 0, second_value = 0;
        if (x + 1 <= n) {
            first_value = dp[x + 1][y];
        }
        if (y - 1 >= 1) {
            second_value = dp[x][y - 1];
        }
        if (first_value >= second_value && x + 1 <= n) {
            x++;
            path += 'F';
        } else {
            y--;
            path += 'R';
        }
    }

    reverse(path.begin(), path.end());

    cout << path << endl;
}