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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
int mbk(long long a,int n,int m){return n?(mbk((a*a)%m,n/2,m)*(n%2?a:1))%m:1;}
int inv(int a,int m){return mbk((long long)a,m-2,m);}
int main(){
  long long a,b,c,d,x,y,z,i,ans=0,M=1e9+7;
  scanf("%lld %lld %lld %lld",&a,&b,&c,&d);
  x=y=1;
  for(i=0;i<b;i++){
    z=inv(i+1,M);//printf("%lld %lld %lld\n",x,y,z);
    x=((x*(a+i  ))%M*z)%M;
    y=((y*(c+i+1))%M*z)%M;//printf("%lld %lld\n",x,y);
  }printf("%lld %lld\n",x,y);
  for(i=b;i<=d;i++){//printf("!!%lld %lld\n",y,x);
    //ans=((ans+y)%M+M-x)%M;printf("%lld\n",ans);
    z=inv(i+1,M);
    y=(y*(c+i+1)%M*z)%M;
    x=(x*(a+i  )%M*z)%M;
    ans=((ans+y)%M+M-x)%M;//printf("%lld\n",ans);
  }
  printf("%lld\n",ans);
  return 0;
}
   
//   ans=((ans+y)%M+M-x)%M;printf("%lld\n",ans);