#include <bits/stdc++.h>
using namespace std;
typedef int64_t LL;
const LL MOD=1e9+7;
LL bnm(int n,int k,LL mod)
{
  LL coef=1;
  vector<LL> sieve(n+1,0);
  if(n==k||k==0){coef=1;return coef;}
  k=min(k,n-k);
  for(LL p=2;p<=n;p++)
  {
    if(sieve.at(p)==0)
    {
      for(LL i=p*p;i<=n;i+=p)
      {
        sieve.at(i)=1;
      }
      for(LL r=p;r<=n;r*=p)
      {
        LL cnt=n/r-k/r-(n-k)/r;
        for(LL j=0;j<cnt;j++)
        {
          coef*=p;
          coef%=mod;
        }
      }
    }
  }
  return coef;
}
int main()
{
  int x,y,z;
  cin>>x>>y;
  if((x+y)%3>0){cout<<0<<endl;return 0;}
  z=(x+y)/3;
  x-=z;
  y-=z;
  if(x<0||y<0){cout<<0<<endl;return 0;}
  cout<<bnm(x+y,x,MOD)<<endl;
}
### Prompt

Create a solution in Cpp for 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;
typedef int64_t LL;
const LL MOD=1e9+7;
LL bnm(int n,int k,LL mod)
{
  LL coef=1;
  vector<LL> sieve(n+1,0);
  if(n==k||k==0){coef=1;return coef;}
  k=min(k,n-k);
  for(LL p=2;p<=n;p++)
  {
    if(sieve.at(p)==0)
    {
      for(LL i=p*p;i<=n;i+=p)
      {
        sieve.at(i)=1;
      }
      for(LL r=p;r<=n;r*=p)
      {
        LL cnt=n/r-k/r-(n-k)/r;
        for(LL j=0;j<cnt;j++)
        {
          coef*=p;
          coef%=mod;
        }
      }
    }
  }
  return coef;
}
int main()
{
  int x,y,z;
  cin>>x>>y;
  if((x+y)%3>0){cout<<0<<endl;return 0;}
  z=(x+y)/3;
  x-=z;
  y-=z;
  if(x<0||y<0){cout<<0<<endl;return 0;}
  cout<<bnm(x+y,x,MOD)<<endl;
}
```