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: Wrong Answer)

def kai(n)
	pro = 1
	2.upto(n) do |i|
		pro *= i
	end
	return pro
end

def f(x,y)
	return kai(x+y)/kai(x)/kai(y)
end


r1, c1, r2, c2 = gets.chomp.split(" ").map{|e|e.to_i}

o = f(r1,c1)
sum = 0

r1.upto(r2) do |x|
	o2 = o
	(c1+1).upto(c2) do |y|
		o2 = o2 * (x+y+1) / (y+1)
		p o2
		sum += o2
	end
	o = o * (x+c1+1) / (x+1)
	p o
	sum += o
end

p (sum % (1e+9 + 7))