find min total sum pos (1,1) to pos (n,m)--move right or down with path print.(dynamic programming)

#include <bits/stdc++.h>

using namespace std;
#define ll long long int
const int mx = 105;
int dp[mx][mx];
int n, m;
int arr[mx][mx];

int mn_cost(int i, int j) {
    if (i > n || j > m) {
        return INT_MAX;
    }
    if (i == n and j == m) {
        return arr[i][j];
    }
    if (dp[i][j] != -1) {
        return dp[i][j];
    }
    return dp[i][j] = arr[i][j] + min(mn_cost(i, j + 1), mn_cost(i + 1, j));
}

void path(int i, int j) {
    cout << "(" << i << " " << j << ")" << endl;
    if (i == n and j == m) {
        return;
    }
    int right = mn_cost(i, j + 1);
    int down = mn_cost(i + 1, j);
    if (right <= down) {
        path(i, j + 1);
    } else {
        path(i + 1, j);
    }
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cin >> n >> m;
    memset(dp, -1, sizeof(dp));
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            cin >> arr[i][j];
        }
    }
    cout << mn_cost(1, 1) << endl;
    path(1, 1);
    return 0;
}


input:
3 3
1 2 3
8 1 1
1 9 2