#include <bits/stdc++.h>
using namespace std;

int MOD = 1e9+7;

long power(long a, long b) {
  return b ? power(a * a % MOD, b / 2) * (b % 2 ? a : 1) % MOD : 1;
}

long comb(long a, long b) {
  long x = 1, y = 1;
  for (int i = 1; i <= b; i++) {
    x = x * (a - i + 1) % MOD;
    y = y * i % MOD;
  }
  return x * power(y, MOD - 2) % MOD;
}

int main() {
  int X, Y;
  cin >> X >> Y;
  if ((X + Y) % 3) return cout << 0 << "\n", 0;
  if (X > Y * 2 || Y > X * 2) return cout << 0 << "\n", 0;
  int Z = (X + Y) / 3;
  cout << comb(Z, X - Z) << "\n";
}
### 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 <bits/stdc++.h>
using namespace std;

int MOD = 1e9+7;

long power(long a, long b) {
  return b ? power(a * a % MOD, b / 2) * (b % 2 ? a : 1) % MOD : 1;
}

long comb(long a, long b) {
  long x = 1, y = 1;
  for (int i = 1; i <= b; i++) {
    x = x * (a - i + 1) % MOD;
    y = y * i % MOD;
  }
  return x * power(y, MOD - 2) % MOD;
}

int main() {
  int X, Y;
  cin >> X >> Y;
  if ((X + Y) % 3) return cout << 0 << "\n", 0;
  if (X > Y * 2 || Y > X * 2) return cout << 0 << "\n", 0;
  int Z = (X + Y) / 3;
  cout << comb(Z, X - Z) << "\n";
}
```