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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
 
class FManyManyPaths {
    static void Main(string[] args) {
        long[] rcrc = Console.ReadLine().Trim().Split(' ').Select(a => long.Parse(a)).ToArray();
        long rtn = 0;
        long[] wk = new long[rcrc[3] + 1];
        for (long i = 0;i <= rcrc[2]; i++) {
            for (long j = 0;j <= rcrc[3]; j++) {
                if (i == 0 || j == 0) {
                    wk[j] = 1;
                } else {
                    wk[j] = (wk[j] + wk[j - 1]) % 1000000007;
                }
                if (i >= rcrc[0] && j >= rcrc[1] && i <= rcrc[2] && j <= rcrc[3] ) {
                    rtn += wk[j];
                }
            }
        }
        System.Console.WriteLine(rtn % 1000000007);
    }
}