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: Runtime Error)

import sys
readline = sys.stdin.buffer.readline
r1,c1,r2,c2 = map(int,readline().split())
mod = 10**9+7
def pow(n,p,mod=10**9+7): #繰り返し二乗法(nのp乗)
    res = 1
    while p > 0:
        if p % 2 == 0:
            n = n ** 2 % mod
            p //= 2
        else:
            res = res * n % mod
            p -= 1
    return res % mod
def factrial_memo(n=10**6+1,mod=10**9+7):
    fact = [1, 1]
    for i in range(2, n + 1):
        fact.append((fact[-1] * i) % mod)
    return fact
def fermat_cmb(n, r, mod=10**9+7): #needs pow,factrial_memo(only fact). return nCk
    return fact[n] * pow(fact[r],mod-2) * pow(fact[n-r],mod-2) %mod
fact = factrial_memo()
r1,c1,r2,c2 = r1+1,c1+1,r2+1,c2+1
al = fermat_cmb(r2+c2,r2)
sub_r = fermat_cmb(r1-1+c2,r1-1)
sub_c = fermat_cmb(r2+c1-1,c1-1)
add_rc = fermat_cmb(r1-1+c1-1,r1-1)

al -= sub_r+sub_c
al += add_rc

print(al%mod)