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

    MOD = 10**9+7
    n = r2+c2+2
    fac = [1]*(n+1)
    rev = [1]*(n+1)
    
    for i in range(1,n+1):
      fac[i] = i*fac[i-1]%MOD
      rev[i] = pow(fac[i], MOD-2, MOD)
    
    comb = lambda a,b:(fac[a]*rev[a-b]*rev[b])%MOD
    f = lambda r,c:comb(r+c+2, c+1)

    ans = (f(r2, c2)-f(r2, c1-1)-f(r1-1, c2)+f(r1-1, c1-1))%MOD
    print(ans)


if __name__ == "__main__":
    solve()
