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

const int mod = 1000000007;

int frac(int n){
  if (!n) return 1;
  int ret = (int64_t) n * frac(n - 1) % mod;
  return ret;
}
int comb(int n, int i){
  int a = frac(n), b = frac(i), c = frac(n - i);
  int d = (int64_t) b * c % mod;
  for (int j = 0; j < mod; j++){
    if (a == (int64_t) j * d % mod) return j;
  }
}
int main(){
  int x, y; cin >> x >> y;
  if ((x + y) % 3){
    cout << 0 << endl;
    return 0;
  }
  int m = (2 * x - y) / 3;
  int n = (2 * y - x) / 3;
  if (m < 0 || n < 0){
    cout << 0 << endl;
    return 0;
  }
  cout << comb(m + n, m) << endl;
}
### Prompt

Please formulate a CPP solution 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;

const int mod = 1000000007;

int frac(int n){
  if (!n) return 1;
  int ret = (int64_t) n * frac(n - 1) % mod;
  return ret;
}
int comb(int n, int i){
  int a = frac(n), b = frac(i), c = frac(n - i);
  int d = (int64_t) b * c % mod;
  for (int j = 0; j < mod; j++){
    if (a == (int64_t) j * d % mod) return j;
  }
}
int main(){
  int x, y; cin >> x >> y;
  if ((x + y) % 3){
    cout << 0 << endl;
    return 0;
  }
  int m = (2 * x - y) / 3;
  int n = (2 * y - x) / 3;
  if (m < 0 || n < 0){
    cout << 0 << endl;
    return 0;
  }
  cout << comb(m + n, m) << endl;
}
```