#include <iostream>

using namespace std;

using ll = long long;

constexpr ll M = 1000000007;

ll modpow(ll x, ll p = M - 2) {
  if (p == 0) return 1;
  ll half = modpow(x, p / 2),
     h2 = (half * half) % M;
  return (p % 2 == 0) ? h2 : ((h2 * x) % M);
}

ll comb(ll n, ll r) {
  ll res = 1;
  for (ll i = 0; i < r; i++) {
    res *= n - i;
    res %= M;
    res *= modpow(i + 1);
    res %= M;
  }
  return res;
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  ll x, y;
  cin >> x >> y;
  for (int i = 0; i < 1000000; i++) {
    int j = x - 2 * i;
    if (2 * j != y - i) continue;
    cout << comb(i + j, i) << endl;
    return 0;
  }
  cout << 0 << endl;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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;

constexpr ll M = 1000000007;

ll modpow(ll x, ll p = M - 2) {
  if (p == 0) return 1;
  ll half = modpow(x, p / 2),
     h2 = (half * half) % M;
  return (p % 2 == 0) ? h2 : ((h2 * x) % M);
}

ll comb(ll n, ll r) {
  ll res = 1;
  for (ll i = 0; i < r; i++) {
    res *= n - i;
    res %= M;
    res *= modpow(i + 1);
    res %= M;
  }
  return res;
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  ll x, y;
  cin >> x >> y;
  for (int i = 0; i < 1000000; i++) {
    int j = x - 2 * i;
    if (2 * j != y - i) continue;
    cout << comb(i + j, i) << endl;
    return 0;
  }
  cout << 0 << endl;
}

```