Problem:
Score : 600 points

Problem Statement

Snuke is standing on a two-dimensional plane. In one operation, he can move by 1 in the positive x-direction, or move by 1 in the positive y-direction.

Let us define a function f(r, c) as follows:

f(r,c) := (The number of paths from the point (0, 0) to the point (r, c) that Snuke can trace by repeating the operation above)

Given are integers r_1, r_2, c_1, and c_2.
Find the sum of f(i, j) over all pair of integers (i, j) such that r_1 ≤ i ≤ r_2 and c_1 ≤ j ≤ c_2, and compute this value modulo (10^9+7).

Constraints

1 ≤ r_1 ≤ r_2 ≤ 10^6

1 ≤ c_1 ≤ c_2 ≤ 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

r_1 c_1 r_2 c_2

Output

Print the sum of f(i, j) modulo (10^9+7).

Sample Input 1

1 1 2 2

Sample Output 1

14

For example, there are two paths from the point (0, 0) to the point (1, 1): (0,0) → (0,1) → (1,1) and (0,0) → (1,0) → (1,1), so f(1,1)=2.

Similarly, f(1,2)=3, f(2,1)=3, and f(2,2)=6. Thus, the sum is 14.

Sample Input 2

314 159 2653 589

Sample Output 2

602215194

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>

using namespace std;

const int MOD = 1000000007;
const int MAX = 2100000;

long long fac[MAX], finv[MAX], inv[MAX];

void comInit() {
	fac[0] = fac[1] = inv[1] = finv[0] = finv[1] = 1;
	for (int i = 2; i < MAX; ++i) {
		fac[i] = fac[i - 1] * i % MOD;
		inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
		finv[i] = finv[i - 1] * inv[i] % MOD;
	}
}

long long nCr(int n, int r) {
	if (n < r || n < 0 || r < 0) return 0;
	return fac[n] * (finv[r] * finv[n - r] % MOD) % MOD;
}

int main() {
	comInit();
	int r1, c1, r2, c2; cin >> r1 >> c1 >> r2 >> c2;
	long long ans = 0;
	for (int i = r1; i <= r2; ++i) {
		ans += (nCr(i + c2 + 1, c2) - nCr(i + c1, c1 - 1)) % MOD;
		ans = (ans % MOD + MOD) % MOD;
	}
	cout << ans << endl;

	return 0;
}