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 Julia (0.5.0) (judge verdict: Accepted)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function abmp(a,b,p);if b==0;1;elseif b%2==0;k=abmp(a,div(b,2),p);(k*k)%p;else;(a*abmp(a,b-1,p))%p;end;end;;
function binarr(n,p);z=1;for i in 1:n;z=z*i%p;end;fac=Array{Int}(n+1);inv=Array{Int}(n+1);inv[n+1]=abmp(z,p-2,p)
for i in 0:n-1;inv[n-i]=(inv[n+1-i]*(n-i))%p;end;for i in 0:n;fac[i+1]=(((z*inv[i+1])%p)*inv[n+1-i])%p;end;fac;end;
function euc(a,m)
	b = m
	x = 1
	u = 0
	while b>0
		q = div(a,b)
		tmp = u
		u = x-q*u
		x = tmp
		tmp = b
		b = a-q*b
		a = tmp
	end
	x<0?x+abs(m):x
end

function main()
	p = 10^9+7
	r1,c1,r2,c2 = readline() |> split |> parseMap
	ans = 0
	x = binarr(r2+c1,p)[c1+1]
	for i in 1:c2-c1+1
		x = (x*(r2+c1+i)%p)*euc(c1+i,p)%p
		ans = (ans+x)%p
	end
	y = binarr(r1+c1-1,p)[c1+1]
	for i in 1:c2-c1+1
		y = (y*(r1+c1-1+i)%p)*euc(c1+i,p)%p
		ans = mod(ans-y,p)
	end
	println(ans)
end

main()