Template-sum of two-dimensional tree array (interval modification, interval query)

#include<iostream>
using namespace std;

typedef long long ll;
const int N = 2100;


ll n, m;
ll t1[N][N], t2[N][N];
ll t4[N][N], t3[N][N];

ll lowbit(ll x) {
    
     return x & (-x); }
void Update(ll x, ll y, ll k) {
    
    
	for (ll i = x; i <= n; i += lowbit(i)) {
    
    
		for (ll j = y; j <= m; j += lowbit(j)) {
    
    
			t1[i][j] += k;
			t2[i][j] += x * k;
			t3[i][j] += y * k;
			t4[i][j] += x * y * k;
		}
	}
}
ll sum(ll x, ll y) {
    
    
	ll ans = 0;
	for (ll i = x; i >= 1; i -= lowbit(i)) {
    
    
		for (ll j = y; j >= 1; j -= lowbit(j)) {
    
    
			ans += (x + 1) * (y + 1) * t1[i][j] - (y + 1) * t2[i][j] - (x + 1) * t3[i][j] + t4[i][j];
		}
	}
	return ans;
}
int main() {
    
    

	cin >> n >> m;

	int sign;
	while (cin >> sign) {
    
    
		if (sign == 1) {
    
    		//区间修改
			ll x1, y1, x2, y2, k;
			cin >> x1 >> y1 >> x2 >> y2 >> k;
			Update(x1, y1, k);		//二维差分思想
			Update(x1, y2 + 1, -k);
			Update(x2 + 1, y1, -k);
			Update(x2 + 1, y2 + 1, k);
		}
		else {
    
    		//区间查询
			ll x1, y1, x2, y2;
			cin >> x1 >> y1 >> x2 >> y2;
			ll ans = sum(x2, y2) - sum(x1 - 1, y2) - sum(x2, y1 - 1) + sum(x1 - 1, y1 - 1);
			cout << ans << endl;
		}
	}
	return 0;
}