HackerEarth Even sum in a matrix problem solution

In this HackerEarth Even sum in a matrix problem solution You are given a matrix A containing N X M elements. You are required to find the number of rectangular submatrices of this matrix such that the sum of the elements in each such submatrix is even.

HackerEarth Even sums in a matrix problem solution.

#include<bits/stdc++.h>
using namespace std;

int n,m;
int sum[2002][2002],a[2002][2002];

bitset<2002> bt[2002];
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
        cin >> n >> m;
        for(int i=0;i<n;i++){

                for(int j=0;j<m;j++){
                cin >> a[i][j];
                        sum[i+1][j+1]=a[i][j]%2;

                }
        }
        for(int i=1;i<=n;i++){
                for(int j=1;j<=m;j++){
                        sum[i][j]+=sum[i][j-1];
                }
        }
        for(int i=1;i<=n;i++){
                for(int j=1;j<=m;j++){
                        sum[i][j]+=sum[i-1][j];
                        sum[i][j]%=2;
                        bt[i][j]=sum[i][j];
                }
        }
        long long sol=0;
        for(int i=0;i<n;i++){
                for(int j=i+1;j<=n;j++){
                        int c= ( bt[i] ^ bt[j]).count();
                        int d= m+1-c;
                        sol += c*1ll*(c-1)/2;
                        sol += d*1ll*(d-1)/2;
                }
        }
        cout<<sol<<endl;
}

Second solution

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

const int MAX_N = 2e3 + 14;

bitset<MAX_N> table[MAX_N];

int main() {
    ios::sync_with_stdio(0), cin.tie(0);
    int n, m;
    cin >> n >> m;
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < m; ++j) {
            int x;
            cin >> x;
            table[i + 1][j + 1] = table[i + 1][j] ^ table[i][j] ^ table[i][j + 1] ^ x % 2;
        }
    }
    ll ans = 0;
    for (int i = 0; i <= n; ++i) {
        for (int j = 0; j < i; ++j) {
            int c = (table[i] ^ table[j]).count();
            ans += c * (c - 1) / 2 + (m - c + 1) * (m - c) / 2;
        }
    }
    cout << ans << '\n';
}