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
r1, c1, r2, c2 = list(map(int, input().split()))
MOD = 10 ** 9 + 7

r = (r2 + 1)
l = (r1)
ans = 0

for i in range(0, c2):
    gyaku = pow((i + 2), MOD - 2, MOD)
    r *= (r2 + 1 + (i + 1))
    r *= gyaku
    l *= (r1 + (i + 1))
    l *= gyaku
    r %= MOD
    l %= MOD
    if i >= c1 - 1:
        ans += r
        ans -= l
    ans %= MOD
print(ans % MOD)