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 (GCC 5.4.1) (judge verdict: Accepted)

// ABC 154-F
// 2020.2.9 bal4u

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

typedef long long ll;

#define MOD 1000000007
#define MAX 2000005
int fact[MAX+2] = {1,1};
int inv[MAX+2] = {1,1};
int facinv[MAX+2] = {1,1};

void init() {
    int i;
	for (i = 2; i < MAX; i++) {
		fact[i] = (ll)fact[i-1]*i % MOD;
		inv[i] = -(MOD/i)*(ll)inv[MOD%i] % MOD;
		facinv[i] = (ll)facinv[i-1]*inv[i] % MOD;
	}
}

int comb(int n, int k) {
    if (n < k) return 0;
//	if (k == 0) return 1;
    return (ll)fact[n] * facinv[k] % MOD * facinv[n-k] % MOD;
}

int main()
{
	int i, r, c, r1, r2, c1, c2;
	ll ans;

    init();
	scanf("%d%d%d%d", &r1, &c1, &r2, &c2);
	ans = 0;
	for (r = r1; r <= r2; ++r) {
		ans += comb(c2+1+r, r+1) - comb(c1+r, r+1);
	}
    ans %= MOD;
	if (ans < 0) ans += MOD;
	printf("%d\n", (int)ans);
	return 0;
}