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

int main() {
  int X,Y;
  cin>>X>>Y;
  int N=(X+Y)/3;
  if((X+Y)%3!=0||X<N||Y<N){
    cout<<"0"<<endl;
  }
  else{
    int64_t Z=1;
    
    for(int i=1;i<=X-N;i++){
      Z*=N+1-i;
      Z=Z%1000000007;
      int64_t N=1000000005;
      int64_t a=1,b=0,c=1;
      while(N>0){
        a*=2;
        if(N%a!=0){
          N-=a/2;
          int64_t d=i;
          for(int j=0;j<b;j++){
            d=d*d;
            d=d%1000000007;
          }
          c=c*d;
          c=c%1000000007;
        }
        b++;
      }
      Z=Z*c;
      Z=Z%1000000007;
    }
    
    cout<<Z<<endl;
  }
  
    
}
### Prompt

Please create a solution in cpp to 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() {
  int X,Y;
  cin>>X>>Y;
  int N=(X+Y)/3;
  if((X+Y)%3!=0||X<N||Y<N){
    cout<<"0"<<endl;
  }
  else{
    int64_t Z=1;
    
    for(int i=1;i<=X-N;i++){
      Z*=N+1-i;
      Z=Z%1000000007;
      int64_t N=1000000005;
      int64_t a=1,b=0,c=1;
      while(N>0){
        a*=2;
        if(N%a!=0){
          N-=a/2;
          int64_t d=i;
          for(int j=0;j<b;j++){
            d=d*d;
            d=d%1000000007;
          }
          c=c*d;
          c=c%1000000007;
        }
        b++;
      }
      Z=Z*c;
      Z=Z%1000000007;
    }
    
    cout<<Z<<endl;
  }
  
    
}
```