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).

Examples

Input

1 1 2 2


Output

14


Input

314 159 2653 589


Output

602215194
r1,c1,r2,c2=map(int,input().split())
mod=10**9+7
n=[1]*(r2+c2+3)
for i in range(r2+c2+2):
  n[i+1]=(n[i]*(i+1))%mod
def g(a,b):
  x,y,z=n[a+b],n[a],n[b]
  return (((x*pow(y,mod-2,mod))%mod)*pow(z,mod-2,mod))%mod
print((g(r2+1,c2+1)-g(r2+1,c1)-g(r1,c2+1)+g(r1,c1))%mod)