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: Accepted)

from sys import stdin
import sys
import numpy as np
import collections
from functools import cmp_to_key
import heapq

##  input functions for me
def rsa(sep = ''):
    if sep == '' :
        return input().split() 
    else: return input().split(sep)
def rip(sep = ''):
    if sep == '' :
        return map(int, input().split()) 
    else: return map(int, input().split(sep))
def ria(sep = ''): 
    return list(rip(sep))
def ri(): return int(input())
def rd(): return float(input())
def rs(): return input()
##

def inv(v, mod):
    return pow(v, mod-2, mod)
def main():
    r1, c1, r2, c2 = rip()

    MM = int(2e6+10)
    fact = [0] * MM
    finv = [0] * MM
    fact[0] = 1
    finv[0] = 1
    mod = int(1e9) + 7
    for i in range(1,MM): fact[i] = (fact[i-1] * i % mod)
    '''
    finv[MM-1] = inv(fact[MM-1], mod)
    for i in reversed(range(1,MM-1)):
        finv[i] = finv[i + 1] * (i + 1) % mod
    def sum_naive(r, c):
        #[0, r) * [0, c)
        ret = 0
        for i in range(r):
            ret += fact[i + 1 + c - 1] * finv[i + 1] * finv[c - 1] % mod
        return ret
    def sum(r, c):
        #[0, r) * [0, c)
        ret = fact[r + c] * finv[r] * finv[c] % mod
        ret += -1 + mod
        ret %= mod
        return ret
    '''
    def sum(r, c):
        #[0, r) * [0, c)
        ret = fact[r + c] * inv(fact[r], mod) * inv(fact[c], mod) % mod
        ret += -1 + mod
        ret %= mod
        return ret
    ans = 0
    ans += sum(r2 + 1, c2 + 1)
    ans -= sum(r2 + 1, c1)
    ans -= sum(r1, c2 + 1)
    ans += sum(r1, c1)
    ans %= mod
    print(ans)



if __name__ == "__main__":
    main()