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 9.2.1) (judge verdict: Accepted)

#include <stdio.h>

#define Mod 1000000007

long long div_mod(long long x, long long y, long long z)
{
	if (x % y == 0) return x / y;
	else return (div_mod((1 + x / y) * y - x, (z % y), y) * z + x) / y;
}

long long combination(int n, int k)
{
	int i;
	long long x, y;
	for (i = n, x = 1; i >= n - k + 1; i--) x = x * i % Mod;
	for (i = 2, y = 1; i <= k; i++) y = y * i % Mod;
	return div_mod(x, y, Mod);
}

int main()
{
	int r[2], c[2];
	scanf("%d %d %d %d", &(r[0]), &(c[0]), &(r[1]), &(c[1]));
	printf("%lld\n", (combination(r[1] + c[1] + 2, r[1] + 1) + combination(r[0] + c[0], r[0]) - combination(r[0] + c[1] + 1, r[0]) - combination(r[1] + c[0] + 1, c[0]) + Mod * 2) % Mod);
	fflush(stdout);
	return 0;
}