#include <bits/stdc++.h>
using namespace std;
#define MOD 1000000007
long mypow(long x,long p){
  if(p==0)return 1;
  if(p%2)return mypow(x,p-1)*x%MOD;
  long y=mypow(x,p/2);return y*y%MOD;
}
long inv(long x){
  return mypow(x,MOD-2);
}
long COM(long n,long k){
  long x=1;
  for(long i=1;i<=n;i++)x=x*i%MOD;
  for(long i=1;i<=k;i++)x=x*inv(i)%MOD;
  for(long i=1;i<=n-k;i++)x=x*inv(i)%MOD;
  return x;
}
int main(){
  long x,y;cin>>x>>y;
  if((x+y)%3!=0||x<(x+y)/3||x>2*(x+y)/3){
    cout<<0;return 0;
  }
  cout<<COM((x+y)/3,x-(x+y)/3)<<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;
#define MOD 1000000007
long mypow(long x,long p){
  if(p==0)return 1;
  if(p%2)return mypow(x,p-1)*x%MOD;
  long y=mypow(x,p/2);return y*y%MOD;
}
long inv(long x){
  return mypow(x,MOD-2);
}
long COM(long n,long k){
  long x=1;
  for(long i=1;i<=n;i++)x=x*i%MOD;
  for(long i=1;i<=k;i++)x=x*inv(i)%MOD;
  for(long i=1;i<=n-k;i++)x=x*inv(i)%MOD;
  return x;
}
int main(){
  long x,y;cin>>x>>y;
  if((x+y)%3!=0||x<(x+y)/3||x>2*(x+y)/3){
    cout<<0;return 0;
  }
  cout<<COM((x+y)/3,x-(x+y)/3)<<endl;
}


```