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 comb(n, r):
    if n < r:return 0
    if n < 0 or r < 0:return 0
    return fa[n] * fi[r] % mod * fi[n - r] % mod
r1, c1, r2, c2 = map(int, input().split())
fa = [1] * (r2 + c2 + 3)
fi = [1] * (r2 + c2 + 3)
for i in range(1, r2 + c2 + 3):
    fa[i] = fa[i - 1] * i % mod
    fi[i] = pow(fa[i], mod - 2, mod)
def ans(r, c):
    return fa[r + c + 2] * fi[r + 1] * fi[c + 1] % mod - 1
print((ans(r2, c2) - ans(r2, c1 - 1) - ans(r1 - 1, c2) + ans(r1 - 1, c1 - 1)) % mod)