Problem:
Score : 600 points

Problem Statement

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).

Sample Input 1

1 1 2 2

Sample Output 1

14

For example, there are two paths from the point (0, 0) to the point (1, 1): (0,0) → (0,1) → (1,1) and (0,0) → (1,0) → (1,1), so f(1,1)=2.

Similarly, f(1,2)=3, f(2,1)=3, and f(2,2)=6. Thus, the sum is 14.

Sample Input 2

314 159 2653 589

Sample Output 2

602215194

Solution in Python (3.4.3) (judge verdict: Runtime Error)

Q = 10**9+7
def getInv(N):#Qはmod
    inv = [0] * (N + 1)
    inv[0] = 1
    inv[1] = 1
    for i in range(2, N + 1):
        inv[i] = (-(Q // i) * inv[Q%i]) % Q
    return inv

def getFactorialInv(N):
    inv = [0] * (N + 1)
    inv[0] = 1
    inv[1] = 1
    ret = [1]*(N+1)
    for i in range(2, N + 1):
        inv[i] = (-(Q // i) * inv[Q%i]) % Q
        ret[i] = ret[i-1]*inv[i]%Q
    return ret

def getFactorial(N):
    ret = [1]*(N+1)
    for i in range(2,N+1):
        ret[i] = ret[i-1]*i%Q
    return ret

def main():
    r1, c1, r2, c2 = map( int, input().split())
    F = getFactorial(2*10**6)
    I = getFactorialInv(10**6)

    def G(a, b):
        return F[a+b+2]*I[a+1]%Q*I[b+1]%Q
    
    print( ( G(r2,c2) - G(r2, c1-1) - G(r1-1, c2) + G(r1-1, c1-1))%Q)
if __name__ == '__main__':
    main()