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 Scala (2.11.7) (judge verdict: Runtime Error)

object Main extends App {
  val Array(r1, c1, r2, c2) = io.StdIn.readLine().split(' ').map(_.toInt)

  def prod(l: Int, r: Int): Int = {
    if (l > r) 1
    else if (l == r) l;
    else if (r - l == 1) l * r;
    else {
      val m = (l + r) / 2
      prod(l, m) * prod(m+1, r)
    }
  }
  def fact(n: Int): Int = {
    if (n < 0)  0
    else if (n == 0) 1
    else if (n == 1 || n == 2) n
    else prod(2, n);
  }

  val ans = List((r1,c1), (r1,c2), (r2,c1), (r2,c2)).map{case (r,c) =>
    fact(r+c) / (fact(r) * fact(c))
  }.sum
  println(ans)
}