#include <bits/stdc++.h>
using namespace std;

int main() {
  long x,y,ans,c,m,mod=1000000007;
  cin >> x >> y;
  if ((x+y)%3==0&&min(x,y)*2>=max(x,y)) {
    ans=1;
    for(int i=0;i<min(x,y)-(x+y)/3;i++) {
      ans=ans*((x+y)/3-i)%mod;
      m=i+1;
      c=1;
      for(long j=1;j<=(mod-2);j=j*2) {
        if((mod-2)/j%2==1) c=c*m%mod;
        m=m*m%mod;
      };
      ans=ans*c%mod;
    };
  } else {
    ans=0;
  };
  cout << ans << endl;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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 x,y,ans,c,m,mod=1000000007;
  cin >> x >> y;
  if ((x+y)%3==0&&min(x,y)*2>=max(x,y)) {
    ans=1;
    for(int i=0;i<min(x,y)-(x+y)/3;i++) {
      ans=ans*((x+y)/3-i)%mod;
      m=i+1;
      c=1;
      for(long j=1;j<=(mod-2);j=j*2) {
        if((mod-2)/j%2==1) c=c*m%mod;
        m=m*m%mod;
      };
      ans=ans*c%mod;
    };
  } else {
    ans=0;
  };
  cout << ans << endl;
}
```