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: Runtime Error)

#include<stdio.h>
int main(){
	int r1, r2, c1, c2;
	int f[100000][100000], output = 0;
	int i, j;

	scanf("%d %d %d %d", &r1, &c1, &r2, &c2);

	for (i = 0; i <= r2; i++){
		f[i][0] = 1;
	}

	for (j = 0; j <= c2; j++){
		f[0][j] = 1;
	}

	for (i = 1; i <= r2; i++){
		for (j = 1; j <= c2; j++){
			f[i][j] = f[i][j - 1] + f[i- 1][j];
		}
	}

	for (i = r1; i <= r2; i++){
		for (j = c1; j <= c2; j++){
			output += f[i][j];
		}
	}
	output = output % 1000000007;

	printf("%d\n", output);
	return 0;
}