max path

#include <bits/stdc++.h>
using namespace std;
// 8-D check
const int N = 100;
int n, m;
int grid[N][N];
bool valid (int row, int col) {
    return (row >= 0 && col >= 0 && row < n && col < m);
}
int max_path (int row, int col) {
    // base case

    if (!valid(row, col))
        return false;
    if (row == n - 1 && col == m - 1)
        return grid[row][col];

    // recursive case

    int down = grid[row][col] + max_path(row + 1, col);
    int right = grid[row][col] + max_path(row, col + 1);
    return max(down, right);
}

int main() {

    freopen("/home/hamoudi/Coding/run.in", "r", stdin);

    cin >> n >> m;
    for (int i = 0; i < n; ++i)
        for (int j = 0; j < m; ++j)
            cin >> grid[i][j];

    cout << max_path(0, 0) << '\n';

    return 0;
}