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: Runtime Error)

#include <iostream>
using namespace std;
#define mod 1000000007

long long inv(long long x){
  long long res=1;
  long long k=mod-2;
  long long y=x;
  while(k){
    if(k&1) res=(res*y)%mod;
    y=(y*y)%mod;
    k/=2;
  }
  return res;
}





int main(void){
  long long f[1000005];
  f[0]=1;
  for(int i=1;i<1000005;i++){
    f[i]=(f[i-1]*i)%mod;
  }
  long long r1,c1,r2,c2;
  cin>>r1>>c1>>r2>>c2;
  long long a,b,c,bc;
  long long retval=0;
  for(long long i=r1;i<=r2;i++){
    for(long long j=c1;j<=c2;j++){
      a=f[i+j];
      b=f[i];
      c=f[j];
      bc=(b*c)%mod;
      retval+=(a*inv(bc))%mod;
    }
  }
  cout<<retval%mod<<endl;
  return 0;
}