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 PyPy3 (2.4.0) (judge verdict: Accepted)

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

def nCr_mod_p(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 10 ** 9 + 7
N = 2*10 ** 6 + 10  # N は必要分だけ用意する
fact = [1, 1]  # fact[n] = (n! mod p), 0! = 1! = 1
factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p), 0! = 1! = 1
inv = [0, 1]  # inv[n] = n^(-1) mod p, 0! = 1　だけど便宜上inv[0]=0にしてる

for i in range(2, N + 1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)

sum22 = nCr_mod_p(r2+1+c2+1,r2+1,p) - 1
sum21 = nCr_mod_p(r2+1+c1,r2+1,p) - 1
sum12 = nCr_mod_p(r1+c2+1,c2+1,p) - 1
sum11 = nCr_mod_p(r1+c1,c1,p) - 1

ans = sum22 - sum21 - sum12 + sum11
ans %= p

print(ans)