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

int main(){
  long long int m=1000000007,ans=0;
  int x,y,a,b;
  cin >> x >> y;
  if((x+y)%3==0){ 
    a=(2*y-x)/3;
    b=(2*x-y)/3;
    if(a>=0&&b>=0){
      long long int p=1,q=1;
      for(int i=a+b;i>a;i--){
        p*=i;
        p%=m;
        q*=(i-a);
        q%=m;
      }
      for(int i=0;i<m;i++){
        if(i*q%m==p){
          ans=i;
          break;
        }
      }
    }
  }
  cout << ans << endl;
}
### Prompt

Create a solution in CPP for the following problem:

There is a knight - the chess piece - at the origin (0, 0) of a two-dimensional grid.

When the knight is at the square (i, j), it can be moved to either (i+1,j+2) or (i+2, j+1).

In how many ways can the knight reach the square (X, Y)?

Find the number of ways modulo 10^9 + 7.

Constraints

* 1 \leq X \leq 10^6
* 1 \leq Y \leq 10^6
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


X Y


Output

Print the number of ways for the knight to reach (X, Y) from (0, 0), modulo 10^9 + 7.

Examples

Input

3 3


Output

2


Input

2 2


Output

0


Input

999999 999999


Output

151840682

### Response

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

int main(){
  long long int m=1000000007,ans=0;
  int x,y,a,b;
  cin >> x >> y;
  if((x+y)%3==0){ 
    a=(2*y-x)/3;
    b=(2*x-y)/3;
    if(a>=0&&b>=0){
      long long int p=1,q=1;
      for(int i=a+b;i>a;i--){
        p*=i;
        p%=m;
        q*=(i-a);
        q%=m;
      }
      for(int i=0;i<m;i++){
        if(i*q%m==p){
          ans=i;
          break;
        }
      }
    }
  }
  cout << ans << endl;
}
```