#include<bits/stdc++.h>
using namespace std;
#define int long long
const int M=1000000007;
int a(int A,int B){
  if(B==0)
    return 1;
  if(B%2==1)
    return a(A,B-1)*A%M;
  int C=a(A,B/2);
  return C*C%M;
}
int b(int A,int B){
  int C=1;
  for(int i=A;i<=B;i++)
    C=C*i%M;
  return C;
}
signed main(){
  int X,Y;
  cin>>X>>Y;
  if((X+Y)%3!=0 || X*2<Y || Y*2<X){
    puts("0");
    return 0;
  }
  int A=X-(X+Y)/3,B=Y-(X+Y)/3;
  cout<<b(B+1,A+B)*a(b(1,A)%M,M-2)%M<<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;
#define int long long
const int M=1000000007;
int a(int A,int B){
  if(B==0)
    return 1;
  if(B%2==1)
    return a(A,B-1)*A%M;
  int C=a(A,B/2);
  return C*C%M;
}
int b(int A,int B){
  int C=1;
  for(int i=A;i<=B;i++)
    C=C*i%M;
  return C;
}
signed main(){
  int X,Y;
  cin>>X>>Y;
  if((X+Y)%3!=0 || X*2<Y || Y*2<X){
    puts("0");
    return 0;
  }
  int A=X-(X+Y)/3,B=Y-(X+Y)/3;
  cout<<b(B+1,A+B)*a(b(1,A)%M,M-2)%M<<endl;
}
```