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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

const int MAX=3000000;
const int MOD=1000000007;

long long fac[MAX],finv[MAX],inv[MAX];

void COMinit(){
  fac[0]=fac[1]=1;
  inv[1]=1;
  finv[0]=finv[1]=1;
  for(int i=2;i<MAX;i++){
    fac[i]=fac[i-1]*i%MOD;
    inv[i]=MOD-inv[MOD % i]*(MOD/i)%MOD;
    finv[i]=finv[i-1]*inv[i]%MOD;
  }
}

long long choose(int x,int y){
  if(x<y) return 0;
  if(x<0||y<0) return 0;
  return fac[x]*(finv[y]*finv[x-y]%MOD)%MOD;
}

int main(){
  
  COMinit();
  
  long long r,c,R,C;
  cin >> r >> c >> R >> C;
  
  R++;
  C++;
  cout << (MOD+(choose(R+C,R)+choose(r+c,r)-choose(R+c,c)-choose(r+C,r)))%MOD << endl;
}