#include <iostream>
using namespace std;
typedef long long ll;

ll fac[1000005];
ll ans = 0;

const ll mod = 1e9 + 7;
ll f(ll a, ll x) {
  ll res = 1;
  while(x > 0) {
    if(x & 1) res = res * a % mod;
    a = a * a % mod;
    x >>= 1;
  }
  return res;
}



int main() {
  int x,y;
  cin >> x >> y;

  fac[0] = 1;
  for(int i = 1; i <= max(x,y); i++) fac[i] = fac[i-1] * i % mod;

  for(int i = 0; i <= x; i++) {
    int yy = y - 2 * i;
    if(yy < 0) continue;
    if((i + 2 * yy) == x) {
      ans = (ans + fac[i+yy] * f(fac[i] * fac[yy] % mod,mod-2)) % mod;
    }
  }

  cout << ans << 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;
typedef long long ll;

ll fac[1000005];
ll ans = 0;

const ll mod = 1e9 + 7;
ll f(ll a, ll x) {
  ll res = 1;
  while(x > 0) {
    if(x & 1) res = res * a % mod;
    a = a * a % mod;
    x >>= 1;
  }
  return res;
}



int main() {
  int x,y;
  cin >> x >> y;

  fac[0] = 1;
  for(int i = 1; i <= max(x,y); i++) fac[i] = fac[i-1] * i % mod;

  for(int i = 0; i <= x; i++) {
    int yy = y - 2 * i;
    if(yy < 0) continue;
    if((i + 2 * yy) == x) {
      ans = (ans + fac[i+yy] * f(fac[i] * fac[yy] % mod,mod-2)) % mod;
    }
  }

  cout << ans << endl;
}

```