#include <bits/stdc++.h>
using namespace std;
typedef long long int lint;
#define mod 1000000007
lint fast_sikis(lint a, lint b){
    if(b==0)
        return 1;
    lint x = fast_sikis(a,b/2);
    x=x*x%mod;
    if(b&1) 
        x = x*a%mod;
    
    return x;

}
lint fak(lint a){
    lint sonuc = 1;
    for(lint i=1; i<=a; i++){
        sonuc = (sonuc*i) % mod;
    }
    return sonuc;
}
int main(){
    lint x,y;
    cin >> x >> y;
    if(x>2*y || y>2*x || (2*y-x) % 3 || (2*x-y) % 3){
        cout << "0";
        return 0;
    }

    lint b=2*y -x;
    lint a = 2*x -y;
    a/=3;
    b/=3;
    cout << fak(a+b) * fast_sikis(fak(a), mod-2) % mod * fast_sikis(fak(b), mod-2) % mod << endl;
    return 0;
}
### 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>
using namespace std;
typedef long long int lint;
#define mod 1000000007
lint fast_sikis(lint a, lint b){
    if(b==0)
        return 1;
    lint x = fast_sikis(a,b/2);
    x=x*x%mod;
    if(b&1) 
        x = x*a%mod;
    
    return x;

}
lint fak(lint a){
    lint sonuc = 1;
    for(lint i=1; i<=a; i++){
        sonuc = (sonuc*i) % mod;
    }
    return sonuc;
}
int main(){
    lint x,y;
    cin >> x >> y;
    if(x>2*y || y>2*x || (2*y-x) % 3 || (2*x-y) % 3){
        cout << "0";
        return 0;
    }

    lint b=2*y -x;
    lint a = 2*x -y;
    a/=3;
    b/=3;
    cout << fak(a+b) * fast_sikis(fak(a), mod-2) % mod * fast_sikis(fak(b), mod-2) % mod << endl;
    return 0;
}
```