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

constexpr long MOD = 1000000007;

long mpow(long a, long b) {
  long res = 1;
  while (b > 0) {
    if (b & 1) res = res * a % MOD;
    a = a * a % MOD;
    b /= 2;
  }
  return res;
}

long com(long n, long r) {
  long x = 1, y = 1;
  for (int i = 1; i <= r; i++) {
    x = x * (n - i + 1) % MOD;
    y = y * i % MOD;
  }
  return x * mpow(y, MOD - 2) % MOD;
}

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

constexpr long MOD = 1000000007;

long mpow(long a, long b) {
  long res = 1;
  while (b > 0) {
    if (b & 1) res = res * a % MOD;
    a = a * a % MOD;
    b /= 2;
  }
  return res;
}

long com(long n, long r) {
  long x = 1, y = 1;
  for (int i = 1; i <= r; i++) {
    x = x * (n - i + 1) % MOD;
    y = y * i % MOD;
  }
  return x * mpow(y, MOD - 2) % MOD;
}

int main() {
  int X, Y;
  cin >> X >> Y;
  if ((X + Y) % 3) return cout << 0 << "\n", 0;
  int n = (X + Y) / 3;
  int r = Y - n;
  if (r < 0) return cout << 0 << "\n", 0;
  cout << com(n, r) << "\n";
}
```