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())

n = [1]*(r2+c2+3)
mod = 10**9 + 7
for i in range(r2+c2+2):
    n[i+1] = (n[i]*((i+1)%mod))%mod

def calc(r,c):
    x = n[r+c]%mod
    y = (n[r]*n[c])%mod
    return (x*(pow(y,mod-2,mod)%mod))%mod

ans = calc(r2+1,c2+1)-calc(r2+1,c1)-calc(r1,c2+1)+calc(r1,c1)
ans %= mod

print(ans)