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():
    mod = 10**9+7
    fact = [1, 1]
    for i in range(2, 2*(10**6)+10):
        fact.append(fact[-1]*i % mod)

    r1, c1, r2, c2 = map(int, input().split())
    r1 -= 1
    c1 -= 1

    def calc(r, c):
        return (pow(fact[c+1]*fact[r+1] % mod, mod-2, mod)*fact[r+c+2]-1) % mod

    print((calc(r2, c2)-calc(r1, c2)-calc(r2, c1)+calc(r1, c1)) % mod)


main()