#include<bits/stdc++.h>
using namespace std;
static const int64_t mod=1000000007;
int64_t f(int64_t x,int64_t y){
if(y==0)
  return 1;
  else{
  if(y%2==0){
   return (f(x,y/2)*f(x,y/2))%mod;
  }else{
   return (((x*f(x,y/2))%mod)*f(x,y/2))%mod;
  }
  }
}
int64_t comb(int64_t n,int64_t k){
int64_t N=1;
  for(int64_t i=n-k+1;i<=n;i++)
    N=(N*i)%mod;
  int64_t K=1;
  for(int64_t i=1;i<=k;i++)
    K=(K*i)%mod;
  return (N*f(K,mod-2))%mod;

}
int main(){
int64_t X,Y;
  cin>>X>>Y;
  if((X+Y)%3!=0)
    cout<<0<<endl;
  else{
    if(2*X-Y<0 || 2*Y-X<0)
      cout<<0<<endl;
    else
    cout<<comb((X+Y)/3,(2*X-Y)/3)<<endl;
  }
   return 0;
}
### Prompt

Please create a solution in cpp 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;
static const int64_t mod=1000000007;
int64_t f(int64_t x,int64_t y){
if(y==0)
  return 1;
  else{
  if(y%2==0){
   return (f(x,y/2)*f(x,y/2))%mod;
  }else{
   return (((x*f(x,y/2))%mod)*f(x,y/2))%mod;
  }
  }
}
int64_t comb(int64_t n,int64_t k){
int64_t N=1;
  for(int64_t i=n-k+1;i<=n;i++)
    N=(N*i)%mod;
  int64_t K=1;
  for(int64_t i=1;i<=k;i++)
    K=(K*i)%mod;
  return (N*f(K,mod-2))%mod;

}
int main(){
int64_t X,Y;
  cin>>X>>Y;
  if((X+Y)%3!=0)
    cout<<0<<endl;
  else{
    if(2*X-Y<0 || 2*Y-X<0)
      cout<<0<<endl;
    else
    cout<<comb((X+Y)/3,(2*X-Y)/3)<<endl;
  }
   return 0;
}
```