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 ncr(n, r): 
    p = 10**9 + 7
    # initialize numerator 
    # and denominator 
    num = den = 1 
    for i in range(r): 
        num = (num * (n - i)) % p 
        den = (den * (i + 1)) % p
    return (num * pow(den,  
            p - 2, p)) % p
  
r1, c1, r2, c2 = [int(i) for i in input().split()]
r1 += 1
c1 += 1
r2 += 1
c2 += 1
print((ncr(r2 + c2, c2) - ncr(r2 + c1 -1, c1-1) - ncr(c2+r1-1, r1-1) + ncr(r1+c1-2, c1-1))%(10**9+7))