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
class ModComb:
    def __init__(self, MAX, mod=10 ** 9 + 7):
        fac = [1, 1]
        finv = [1, 1]
        inv = [0, 1]
        for i in range(2, MAX):
            fac.append(fac[i - 1] * i % mod)
            inv.append(mod - inv[mod % i] * (mod // i) % mod)
            finv.append(finv[i - 1] * inv[i] % mod)
        self.fac, self.finv, self.mod = fac, finv, mod

    def nCk(self, n, k):
        if n < k or n < 0 or k < 0:
            return 0
        fac, finv, mod = self.fac, self.finv, self.mod
        return fac[n] * (finv[k] * finv[n - k] % mod) % mod

mod = 10 ** 9 + 7

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

mc = ModComb(r2 + c2 + 10)
def f(i, j):
    return mc.nCk(i + j, i)

print((f(r2 + 1, c2 + 1) - f(r2 + 1, c1) - f(r1, c2 + 1) + f(r1, c1)) % mod)