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
def comb(n,k,mod):
  if n<k:
    return 0
  if n-k<k:
    k=n-k
  c=1
  for x in range(n-k+1,n+1):
    c=(c*x)%mod
  d=1
  for x in range(1,k+1):
    d=(d*x)%mod
  c=c*pow(d,mod-2,mod)
  return c%mod
def f(i,j):
  return comb(i+j,i,mod)
ans=f(r2+1,c2+1)-f(r2+1,c1)-f(r1,c2+1)+f(r1,c1)
ans%=mod
print(ans)
