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
def main():
  M=10**9+7
  a,b,c,d=map(int,input().split())
  n=c+d+2
  fac=[0]*(n+1)
  fac[0]=lt=1
  for i in range(1,n+1):fac[i]=lt=lt*i%M
  inv=[0]*(n+1)
  inv[n]=lt=pow(fac[n],M-2,M)
  for i in range(n,0,-1):inv[i-1]=lt=lt*i%M
  comb=lambda n,k:fac[n]*inv[n-k]*inv[k]
  f=lambda r,c:fac[r+c+2]*inv[c+1]*inv[r+1]-c-r-2
  print((f(c,d)-f(c,b-1)-f(a-1,d)+f(a-1,b-1))%M)
main()