#include <bits/stdc++.h>

const int MOD = 1e9 + 7;

long long inv(long long a, long long b){
  return 1 < a ? b - inv(b % a, a) * b / a : 1;
}

int choose(int n, int k) {

  int max = std::max(n, k);
  std::vector<int> fat(max + 1);

  fat[0] = 1;
  for (int i = 1; i <= max; i++)
    fat[i] = 1LL * fat[i-1] * i % MOD;

  return (1LL * fat[n] * inv(fat[k], MOD) % MOD) * inv(fat[n-k], MOD) % MOD;
}

int main() {
  int x, y;
  scanf("%d%d", &x, &y);

  if ((x + y) % 3)
    return puts("0"), 0;

  int n = (x + y) / 3;

  if (x < n || y < n)
    return puts("0"), 0;

  int k = y - n;
  
  printf("%d\n", choose(n, k));
}

### Prompt

Create a solution in Cpp for 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>

const int MOD = 1e9 + 7;

long long inv(long long a, long long b){
  return 1 < a ? b - inv(b % a, a) * b / a : 1;
}

int choose(int n, int k) {

  int max = std::max(n, k);
  std::vector<int> fat(max + 1);

  fat[0] = 1;
  for (int i = 1; i <= max; i++)
    fat[i] = 1LL * fat[i-1] * i % MOD;

  return (1LL * fat[n] * inv(fat[k], MOD) % MOD) * inv(fat[n-k], MOD) % MOD;
}

int main() {
  int x, y;
  scanf("%d%d", &x, &y);

  if ((x + y) % 3)
    return puts("0"), 0;

  int n = (x + y) / 3;

  if (x < n || y < n)
    return puts("0"), 0;

  int k = y - n;
  
  printf("%d\n", choose(n, k));
}

```