#include<bits/stdc++.h>
using namespace std;
#define ll long long int
int r1,r2,c1,c2;
const int maxN=1e6,M=1e9+7;
ll iv[3*maxN],f1[3*maxN],f2[3*maxN];
 
ll nck(int n,int k){
  return f1[n]*f2[k]%M*f2[n-k]%M;
}
 
int main(){
  iv[1]=1;
  for(int i=2;i<3*maxN;i++)
    	iv[i]=M-M/i*iv[M%i]%M;
  f1[0]=f2[0]=1;
  for(int i=1;i<3*maxN;i++){
    f1[i]=f1[i-1]*i%M;
    f2[i]=f2[i-1]*iv[i]%M;
  }
  cin>>r1>>c1>>r2>>c2; 
  cout<<((nck(r2+c2+2,c2+1)-nck(r1+c2+1,c2+1)-nck(r2+c1+1,c1)+nck(r1+c1,c1)%M+M)%M);
  return 0;
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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).

Examples

Input

1 1 2 2


Output

14


Input

314 159 2653 589


Output

602215194

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
#define ll long long int
int r1,r2,c1,c2;
const int maxN=1e6,M=1e9+7;
ll iv[3*maxN],f1[3*maxN],f2[3*maxN];
 
ll nck(int n,int k){
  return f1[n]*f2[k]%M*f2[n-k]%M;
}
 
int main(){
  iv[1]=1;
  for(int i=2;i<3*maxN;i++)
    	iv[i]=M-M/i*iv[M%i]%M;
  f1[0]=f2[0]=1;
  for(int i=1;i<3*maxN;i++){
    f1[i]=f1[i-1]*i%M;
    f2[i]=f2[i-1]*iv[i]%M;
  }
  cin>>r1>>c1>>r2>>c2; 
  cout<<((nck(r2+c2+2,c2+1)-nck(r1+c2+1,c2+1)-nck(r2+c1+1,c1)+nck(r1+c1,c1)%M+M)%M);
  return 0;
}
```