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