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():
  r1,c1,r2,c2 = map(int,input().split())

  mod = 10**9+7

  fact = [1,1]
  finv = [1,1]
  inv = [0,1]

  for i in range(2,r2+c2+3):
    fact.append((fact[-1]*i)%mod)
    inv.append((inv[mod%i]*(mod-mod//i))%mod)
    finv.append((finv[-1]*inv[-1])%mod)

  def nCr(n,r,mod):
      
      return fact[n]*finv[r]*finv[n-r]%mod

  print((nCr(r2+c2+2,r2+1,mod)+nCr(r1+c1,r1,mod)-nCr(c2+r1+1,r1,mod)-nCr(r2+c1+1,c1,mod))%mod)

if __name__ == "__main__":
  main()