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

fac = [1]
inv = [1]
for i in range(1, r2 + c2 + 10) :
  fac.append(fac[-1] * i % mod)
  inv.append(pow(fac[-1], mod - 2, mod))

def comb(n, r) :
  return fac[n] * inv[n-r] * inv[r] % mod

def g(x, y) :
  return comb(x + y, y)

ret = g(r2+1, c2+1) - g(r2+1, c1) - g(r1, c2+1) + g(r1, c1)
ret %= mod

print(ret)