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: Runtime Error)

using System;
using System.Linq;

class Program {
  public static void Main() {
    int[] input = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
    int xa = input[0], ya = input[1], xb = input[2], yb = input[3];
    
    long total = 0;
    
    for (int i = xa; i <= xb; i++) {
      for (int j = ya; j <= yb; j++) {
        total += Kaizyo(i + j) / (Kaizyo(i) * Kaizyo(j));
      }
    }
    
    Console.WriteLine(total);
  }
  
  public static long Kaizyo(int n) {
    long fact;
    
    if (n == 0)
      fact = 1;
    else
      fact = n * Kaizyo(n - 1);
    
    return fact;
  }
}