#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll M = 1e9 + 7;

int x, y;

int main () {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> x >> y;
  int a = (2 * x - y) / 3, b = (2 * y - x) / 3;
  if ((x+y)%3 || a < 0 || b < 0) {
    cout << 0 << endl;
    return 0;
  }
  ll D = 1, d = 1, m = min(a, b), n = a + b;
  for (int i = 0; i < m; ++i) {
    D = D * (n-i) % M;
    d = d * (i+1) % M;
  }
  // d^-1 mod M = d^M-2 mod M
  ll p = M-2, id = 1;
  while (p != 0) {
    if (p%2 == 0) {
      d = d * d % M;
      p /= 2;
    } else {
      id = id * d % M;
      p -= 1;
    }
  }
  cout << (D * id % M) << 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;
typedef long long ll;
const ll M = 1e9 + 7;

int x, y;

int main () {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> x >> y;
  int a = (2 * x - y) / 3, b = (2 * y - x) / 3;
  if ((x+y)%3 || a < 0 || b < 0) {
    cout << 0 << endl;
    return 0;
  }
  ll D = 1, d = 1, m = min(a, b), n = a + b;
  for (int i = 0; i < m; ++i) {
    D = D * (n-i) % M;
    d = d * (i+1) % M;
  }
  // d^-1 mod M = d^M-2 mod M
  ll p = M-2, id = 1;
  while (p != 0) {
    if (p%2 == 0) {
      d = d * d % M;
      p /= 2;
    } else {
      id = id * d % M;
      p -= 1;
    }
  }
  cout << (D * id % M) << endl;
}
```