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 = map(int,input().split())
mod = 10**9+7

def p_mod(m,n,p):
    a = 1
    for i in range(n):
        a = a*(m-i) % p
    return a

def c_mod(m,n,p):
    return (p_mod(m,n,p)*pow(p_mod(n,n,p),p-2,p)) % p

print((c_mod(r2+c2+2,r2+1,mod) - c_mod(r1+c2+1,r1,mod) - c_mod(r2+c1+1,c1,mod) + c_mod(r1+c1,r1,mod)) % mod)