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 Ruby (2.3.3) (judge verdict: Accepted)

M=10**9+7

class Combination
  def initialize(n, m=10**9+7)
    @m = m
    @fact, @inv, @finv = Array.new(3){[1, 1]}
    2.upto(n) do |i|
      @fact[i] = (@fact[i-1] * i) % @m
      @inv[i]  = (@inv[@m % i] * (@m - @m / i) ) % @m
      @finv[i] = (@finv[i-1] * @inv[i] ) % @m
    end
  end
  def query(n, r)
    return 0 if (n < r) || (n < 0) || (r < 0)
    (@fact[n] * @finv[n-r] % @m) * @finv[r] % @m
  end
end

def sum(n, r)
  C.query(n+r+2, r+1) - 1
end

r1,c1,r2,c2=gets.split.map(&:to_i)
r1-=1
c1-=1
C=Combination.new(r2+c2+2, M)
ans = 0
ans += sum(r2, c2)
ans -= sum(r1, c2)
ans -= sum(r2, c1)
ans += sum(r1, c1)
ans %= M
p (ans + M) % M