#include <iostream>
#include <cmath>
using namespace std;
int main(){
  int BIG = 1000000007;
  int X;
  int Y;
  cin >> X >> Y;
  if((X + Y) % 3 != 0){
    cout << 0 << endl;
    return 0;
  }
  int a = (2 * X - Y);
  int b = (2 * Y - X);
  a /= 3;
  b /= 3;
  if(a < 0 || b < 0){
    cout << 0 << endl;
    return 0;
  }
  long long int power1 = 1;
  long long int quotient1 = 1;
  for(int i = (a+1); i <= a+b; i++){
    power1 *= i;
    quotient1 *= (i-a);
    power1 %= BIG;
    quotient1 %= BIG;
  }
  for(int i = 0; i < 1000000007; i++){
    if(i * quotient1 % BIG == power1){
      cout << i << endl;
      return 0;
    }
  }


}
### Prompt

Generate a CPP solution 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 <iostream>
#include <cmath>
using namespace std;
int main(){
  int BIG = 1000000007;
  int X;
  int Y;
  cin >> X >> Y;
  if((X + Y) % 3 != 0){
    cout << 0 << endl;
    return 0;
  }
  int a = (2 * X - Y);
  int b = (2 * Y - X);
  a /= 3;
  b /= 3;
  if(a < 0 || b < 0){
    cout << 0 << endl;
    return 0;
  }
  long long int power1 = 1;
  long long int quotient1 = 1;
  for(int i = (a+1); i <= a+b; i++){
    power1 *= i;
    quotient1 *= (i-a);
    power1 %= BIG;
    quotient1 %= BIG;
  }
  for(int i = 0; i < 1000000007; i++){
    if(i * quotient1 % BIG == power1){
      cout << i << endl;
      return 0;
    }
  }


}
```