#include <iostream>

using namespace std;
using ll = long long;

ll mod = 1000000007;

ll modinv(ll a) {
  ll n = mod - 2;
  ll res = 1;
  while (0 < n) {
    if (n & 1) res = res * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return res;
}

int main() {
  ll x, y;
  cin >> x >> y;
  ll a = (2 * y - x) / 3;
  ll b = y - 2 * a;

  ll res = 0 <= a && 0 <= b && a + 2 * b == x && 2 * a + b == y;
  for (ll i = 0; i < a + b; ++i)
    res = res * (a + b - i) % mod;
  for (ll i = 0; i < a; ++i)
    res = res * modinv(a - i) % mod;
  for (ll i = 0; i < b; ++i)
    res = res * modinv(b - i) % mod;
  cout << res << endl;
}
### Prompt

Please create a solution in CPP 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;
using ll = long long;

ll mod = 1000000007;

ll modinv(ll a) {
  ll n = mod - 2;
  ll res = 1;
  while (0 < n) {
    if (n & 1) res = res * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return res;
}

int main() {
  ll x, y;
  cin >> x >> y;
  ll a = (2 * y - x) / 3;
  ll b = y - 2 * a;

  ll res = 0 <= a && 0 <= b && a + 2 * b == x && 2 * a + b == y;
  for (ll i = 0; i < a + b; ++i)
    res = res * (a + b - i) % mod;
  for (ll i = 0; i < a; ++i)
    res = res * modinv(a - i) % mod;
  for (ll i = 0; i < b; ++i)
    res = res * modinv(b - i) % mod;
  cout << res << endl;
}
```