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
from functools import reduce
def C(n,r):
    if not 0<=r<=n: return 0
    r=min(r,n-r)
    N=reduce(lambda x,y: x*y%M, range(n,n-r,-1),1)
    D=reduce(lambda x,y: x*y%M, range(1,r+1),1)
    return N*pow(D,M-2,M)%M
def f(r,c): return C(r+c,c)
M=10**9+7
a,b,c,d=map(int, input().split())
print((f(c+1,d+1)-f(a,d+1)-f(c+1,b)+f(a,b))%M)