#include<bits/stdc++.h>
using namespace std;
#define MOD 1000000007

int main() {

  int X,Y;
  cin >> X >> Y;

  if((X+Y) % 3 != 0 || 2*Y < X || Y > 2*X) {
    cout << 0 << endl;
    return 0;
  }

  int x = (X-2*Y) / (-3);
  int y = (X-x) / 2;

  vector<long long> fac(2000100,1),finv(2000100,1),inv(2000100,1);
  for(int i = 2;i < 2000100;i++) {
    fac.at(i) = fac.at(i-1) * i % MOD;
    inv.at(i) = MOD - inv.at(MOD % i) * (MOD/i) % MOD;
    finv.at(i) = finv.at(i-1) * inv.at(i) % MOD;
  }

  cout << fac.at(x+y) * (finv.at(x) * finv.at(y) % MOD) % MOD << endl;
}



### 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;
#define MOD 1000000007

int main() {

  int X,Y;
  cin >> X >> Y;

  if((X+Y) % 3 != 0 || 2*Y < X || Y > 2*X) {
    cout << 0 << endl;
    return 0;
  }

  int x = (X-2*Y) / (-3);
  int y = (X-x) / 2;

  vector<long long> fac(2000100,1),finv(2000100,1),inv(2000100,1);
  for(int i = 2;i < 2000100;i++) {
    fac.at(i) = fac.at(i-1) * i % MOD;
    inv.at(i) = MOD - inv.at(MOD % i) * (MOD/i) % MOD;
    finv.at(i) = finv.at(i-1) * inv.at(i) % MOD;
  }

  cout << fac.at(x+y) * (finv.at(x) * finv.at(y) % MOD) % MOD << endl;
}



```