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
mod = 10**9 + 7

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

def inv(x):
  m = mod
  u = 1
  v = 0
  while(m):
    t = x // m
    x -= t * m
    x, m = m, x
    u -= t * v
    u, v = v, u
  u %= mod
  if u < 0:
    u += mod
  return u

fac = [1]
for i in range(1, r2 + c2 + 3):
  fac.append(fac[i - 1] * i % mod)

def paths(r, c):
  return fac[r + c + 2] * inv(fac[r + 1] * fac[c + 1]) % mod

f = paths(r2, c2) - paths(r2, c1 - 1) - paths(r1 - 1, c2) + paths(r1 - 1, c1 - 1)
f %= mod
if f < 0:
   f += mod
print(f)