#include <bits/stdc++.h>
using namespace std;
using ll=long long;
const ll mod=1e9+7;

int main(){
  int X,Y; cin>>X>>Y;
  
  if((2*Y-X)%3||(2*X-Y)%3||X*2<Y||Y*2<X){
    cout<<0<<endl;
  }else{
    int a=(2*Y-X)/3;
    int b=(2*X-Y)/3;
    if(a<b) swap(a,b);
    
    ll nx=a+1,dx=1,n=1,d=1;
    while(b>0){
      n=n*nx%mod;
      d=d*dx%mod;
      nx++,dx++,b--;
    }
    ll e=mod-2;
    dx=d,d=1;
    while(e>0){
      if(e&1){
        d=d*dx%mod;
      }
      dx=dx*dx%mod;
      e>>=1;
    }
    cout<<n*d%mod<<endl;
  }
}
### Prompt

Your task is to create a cpp solution 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;
using ll=long long;
const ll mod=1e9+7;

int main(){
  int X,Y; cin>>X>>Y;
  
  if((2*Y-X)%3||(2*X-Y)%3||X*2<Y||Y*2<X){
    cout<<0<<endl;
  }else{
    int a=(2*Y-X)/3;
    int b=(2*X-Y)/3;
    if(a<b) swap(a,b);
    
    ll nx=a+1,dx=1,n=1,d=1;
    while(b>0){
      n=n*nx%mod;
      d=d*dx%mod;
      nx++,dx++,b--;
    }
    ll e=mod-2;
    dx=d,d=1;
    while(e>0){
      if(e&1){
        d=d*dx%mod;
      }
      dx=dx*dx%mod;
      e>>=1;
    }
    cout<<n*d%mod<<endl;
  }
}
```