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())

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

total = fact[r2 + c2 + 2] * inv_fact[r2 + 1] * inv_fact[c2 + 1] % mod
total -= fact[r1 + c2 + 1] * inv_fact[r1] * inv_fact[c2 + 1] % mod
total -= fact[r2 + c1 + 1] * inv_fact[c1] * inv_fact[r2 + 1] % mod
total += fact[r1 + c1] * inv_fact[r1] * inv_fact[c1] % mod

print(total % mod)