#include<bits/stdc++.h>
using namespace std;
long modpow(long a,long n,long mod){
  long ans=1;
  while (n>0){
    if(n&1) ans=ans*a%mod;
    a=a*a%mod;
    n=n/2;
  }
  return ans; 
}
long modinv(long a,long mod){
  return modpow(a,mod-2,mod);
}
int main(){
  long x,y;cin>>x>>y;
  long a,b,ans,mod,memo;
  mod=1000000007;
  ans=1; memo=1;
  a=(2*x-y)/3; b=(2*y-x)/3;
   
  if( (x+y)%3!=0 || a<0 || b<0 ) cout<<0;
  
  else{   
    for(long i=1;i<=a+b;i++) ans=ans*i%mod;
    for(long i=1;i<=a;i++) memo=memo*i%mod;
    for(long i=1;i<=b;i++) memo=memo*i%mod;    
    memo=modinv(memo,mod);
    cout<<ans*memo%mod;
  }
}
### Prompt

Develop a solution in cpp to the problem described below:

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;
long modpow(long a,long n,long mod){
  long ans=1;
  while (n>0){
    if(n&1) ans=ans*a%mod;
    a=a*a%mod;
    n=n/2;
  }
  return ans; 
}
long modinv(long a,long mod){
  return modpow(a,mod-2,mod);
}
int main(){
  long x,y;cin>>x>>y;
  long a,b,ans,mod,memo;
  mod=1000000007;
  ans=1; memo=1;
  a=(2*x-y)/3; b=(2*y-x)/3;
   
  if( (x+y)%3!=0 || a<0 || b<0 ) cout<<0;
  
  else{   
    for(long i=1;i<=a+b;i++) ans=ans*i%mod;
    for(long i=1;i<=a;i++) memo=memo*i%mod;
    for(long i=1;i<=b;i++) memo=memo*i%mod;    
    memo=modinv(memo,mod);
    cout<<ans*memo%mod;
  }
}
```