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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		Scanner scanner = new Scanner(System.in);

		int r1 = scanner.nextInt();
		int c1 = scanner.nextInt();
		int r2 = scanner.nextInt() + 1;
		int c2 = scanner.nextInt() + 1;

		long sum = (f(r2, c2) - f(r1, c2) - f(r2, c1) + f(r1, c1)) % PRIME;

		if (sum < 0)
			sum += PRIME;

		System.out.println(sum);

		scanner.close();
	}

	static long f(int r, int c) {
		return fact(r + c) * inverse(fact(r) * fact(c) % PRIME) % PRIME;
	}

	static long fact(int n) {
		if (n == 0)
			return 1;
		return fact(n - 1) * n % PRIME;
	}

	static int inverse(long denom) {
		if (denom == 0)
			return 0;

		int a = PRIME;
		int b = (int) denom;
		int x = 0;
		int y = 1;
		int temp;

		while (a % b != 0) {
			x -= a / b * y;
			temp = x;
			x = y;
			y = temp;
			temp = a % b;
			a = b;
			b = temp;
		}

		//		while (y < 0)
		//			y += PRIME;

		return y;
	}

	static final int PRIME = 1000000007;
}