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


def inv(x):
    return pow(x, mod - 2, mod)


r1, c1, r2, c2 = map(int, input().split())
fact, inv_fact = [1, 1], [1, 1]
for i in range(2, r2+c2+3):
    fact.append(fact[-1] * i % mod)
    inv_fact.append(inv(fact[-1]))


def nCr(n, r):
    return fact[n] * inv_fact[r] * inv_fact[n-r] % mod


def path_sum_sum(r, c):
    return ((r + 2) * nCr(c+r+2, r+2) % mod + mod - c - 1) * inv(c + 1) % mod


ans = (path_sum_sum(r2, c2) + mod - path_sum_sum(r2, c1-1) +
       mod - path_sum_sum(r1-1, c2) + path_sum_sum(r1-1, c1-1))
print(ans % mod)
