Maximum Sum with number of ways

#include <bits/stdc++.h>

using namespace std;

const int N = 205;

int n, m;
long long a[N][N], dp[N][N], cnt[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];
        }
    }

    for (int i = 1; i <= m; i++) {
        dp[1][i] = a[1][i];
        cnt[1][i] = 1;
    }

    for (int i = 2; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            int mx = dp[i - 1][j];
            if (j - 1 >= 1 && mx < dp[i - 1][j - 1]) {
                mx = dp[i - 1][j - 1];
            }
            if (j + 1 <= m && mx < dp[i - 1][j + 1]) {
                mx = dp[i - 1][j + 1];
            }

            dp[i][j] = mx + a[i][j];
            if (j - 1 >= 1 && dp[i - 1][j - 1] == mx) {
                cnt[i][j] += cnt[i - 1][j - 1];
            }
            if (dp[i - 1][j] == mx) {
                cnt[i][j] += cnt[i - 1][j];
            }
            if (j + 1 <= m && dp[i - 1][j + 1] == mx) {
                cnt[i][j] += cnt[i - 1][j + 1];
            }
        }
    }

    long long mx = dp[n][1];

    for (int i = 2; i <= m; i++) {
        mx = max(mx, dp[n][i]);
    }

    cout << mx << " ";

    long long cn = 0;

    for (int i = 1; i <= m; i++) {
        if (dp[n][i] == mx) cn += cnt[n][i];
    }

    cout << cn << endl;
}