#include <iostream>

using namespace std;

#define int long long

int pow(int v, int p);

signed main() {
  int X, Y;
  cin >> X >> Y;
  int ans = 0;
  const int m = 1e9+7;
  for (int i = 0; i <= X; i++) {
    int x = X - i;
    int y = Y - i * 2;
    if (y * 2 != x) continue;
    int s = i+y;
    int t = 1;
    int u = 1;
    for (int j = 1; j <= i; j++) {
      t = (t * s) % m;
      u = (u * j) % m;
      s--;
    }
    ans += t * pow(u, m-2) % m;
    ans %= m;
  }
  cout << ans << endl;
  return 0;
}

int pow(int v, int p) {
  const int m = 1e9+7;
  if (p==0) return 1;
  if (p%2==0) return pow(v*v%m,p/2);
  return v*pow(v,p-1)%m;
}
### Prompt

Your challenge is to write 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>

using namespace std;

#define int long long

int pow(int v, int p);

signed main() {
  int X, Y;
  cin >> X >> Y;
  int ans = 0;
  const int m = 1e9+7;
  for (int i = 0; i <= X; i++) {
    int x = X - i;
    int y = Y - i * 2;
    if (y * 2 != x) continue;
    int s = i+y;
    int t = 1;
    int u = 1;
    for (int j = 1; j <= i; j++) {
      t = (t * s) % m;
      u = (u * j) % m;
      s--;
    }
    ans += t * pow(u, m-2) % m;
    ans %= m;
  }
  cout << ans << endl;
  return 0;
}

int pow(int v, int p) {
  const int m = 1e9+7;
  if (p==0) return 1;
  if (p%2==0) return pow(v*v%m,p/2);
  return v*pow(v,p-1)%m;
}
```