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: Runtime Error)

import java.util.*;

public class Main {
    public static void main(String args[]) throws Exception {
        Scanner sc = new Scanner(System.in);
        int MOD = 1000000007;

        int r1 = sc.nextInt();
        int c1 = sc.nextInt();
        int r2 = sc.nextInt();
        int c2 = sc.nextInt();

        long[][] dp = new long[r2 + 1][c2 + 1];
        dp[0][0] = 1;
        for(int i = 1; i <= r2; i++)
        	dp[i][0] = 1;
        for(int i = 1; i <= c2; i++)
        	dp[0][i] = 1;

        for(int i = 1; i <= r2; i++) {
        	for(int j = 1; j <= c2; j++)
        		dp[i][j] = (dp[i-1][j] + dp[i][j-1]) % MOD;
        }
        long sum = 0;
        for(int i = r1; i <= r2; i++)
        	for(int j = c1; j <= c2; j++)
        		sum += (dp[i][j] % MOD);
        System.out.println(sum % MOD);
    }
}