#include <bits/stdc++.h>
using namespace std;
using ll =long long;
#define all(v) v.begin(),v.end()
 
ll mod_pow(ll x,ll n,ll mod) {
ll res=1;
  while(n>0) {
if(n&1) {
res=res*x%mod;
}
  x=x*x%mod;
    n>>=1;
  }
  return res;
}
 


int main() {
  ll X,Y;
  cin>>X>>Y;
  if(X>2*Y||Y>2*X) {
    cout<<0<<endl;
    return 0;

  }
  else if((X+Y)%3!=0) {
cout<<0<<endl;
    return 0;
  }
  
  ll A=(X+Y)/3;
  ll B=X-A;
  
  
  ll mod=1000000007;
  ll ans=1;
  for(ll i=0;i<B;i++) {
ans*=(A-i);
    ans%=mod;
  }
  
  for(ll i=2;i<=B;i++) {
ans*=mod_pow(i,mod-2,mod)%mod;
    ans%=mod;
  }
  
  cout<<ans<<endl;
}
    
    

  
  
  
  
  
  
  
  
  
  
  
  
### Prompt

Construct a CPP code solution to the problem outlined:

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;
#define all(v) v.begin(),v.end()
 
ll mod_pow(ll x,ll n,ll mod) {
ll res=1;
  while(n>0) {
if(n&1) {
res=res*x%mod;
}
  x=x*x%mod;
    n>>=1;
  }
  return res;
}
 


int main() {
  ll X,Y;
  cin>>X>>Y;
  if(X>2*Y||Y>2*X) {
    cout<<0<<endl;
    return 0;

  }
  else if((X+Y)%3!=0) {
cout<<0<<endl;
    return 0;
  }
  
  ll A=(X+Y)/3;
  ll B=X-A;
  
  
  ll mod=1000000007;
  ll ans=1;
  for(ll i=0;i<B;i++) {
ans*=(A-i);
    ans%=mod;
  }
  
  for(ll i=2;i<=B;i++) {
ans*=mod_pow(i,mod-2,mod)%mod;
    ans%=mod;
  }
  
  cout<<ans<<endl;
}
    
    

  
  
  
  
  
  
  
  
  
  
  
  
```