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) throws Exception {
		Scanner sc = new Scanner(System.in);
		int r1 = sc.nextInt() - 1;
		int c1 = sc.nextInt() - 1;
		int r2 = sc.nextInt();
		int c2 = sc.nextInt();
		sc.close();

		int mod = 1000000007;
		long a = nCr(r2 + c2 + 2, c2 + 1, mod) - 1;
		long b = nCr(r1 + c2 + 2, c2 + 1, mod) - 1;
		long c = nCr(r2 + c1 + 2, c1 + 1, mod) - 1;
		long d = nCr(r1 + c1 + 2, c1 + 1, mod) - 1;
		long ans = a - b - c + d + mod + mod;
		ans %= mod;
		System.out.println(ans);
	}

	static long nCr(int n, int r, int m) {
		long val = 1;
		for (int i = 1; i <= r; i++) {
			val = val * (n - i + 1) % m;
			val = val * modinv(i, m) % m;
		}
		return val;
	}

	static long modinv(long a, int m) {
		long b = m;
		long u = 1;
		long v = 0;
		long tmp = 0;

		while (b > 0) {
			long t = a / b;
			a -= t * b;
			tmp = a;
			a = b;
			b = tmp;

			u -= t * v;
			tmp = u;
			u = v;
			v = tmp;
		}

		u %= m;
		if (u < 0) u += m;
		return u;
	}
}