#include<bits/stdc++.h>
using namespace std;
int main(){
    int x,y;
    cin>>x>>y;
    if((x+y)%3){
        cout<<"0"<<endl;
        return 0;
    }
    int n=(x+y)/3,r=x-n;//nCr
    if(r<0 || r>n){
        cout<<"0"<<endl;
        return 0;
    }
    if(r==0 || r==n){
        cout<<"1"<<endl;
        return 0;
    }
    const int mod=1000000007;
    long long a=1;
    for(int i=1;i<=r;i++){
        a*=i;
        a%=mod;
    }
    long long b=a;
    a=1;
    for(int i=mod-2;i;i/=2){
        if(i%2){
            a*=b;
            a%=mod;
        }
        b*=b;
        b%=mod;
    }
    for(int i=n;i>n-r;i--){
        a*=i;
        a%=mod;
    }
    cout<<a<<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;
int main(){
    int x,y;
    cin>>x>>y;
    if((x+y)%3){
        cout<<"0"<<endl;
        return 0;
    }
    int n=(x+y)/3,r=x-n;//nCr
    if(r<0 || r>n){
        cout<<"0"<<endl;
        return 0;
    }
    if(r==0 || r==n){
        cout<<"1"<<endl;
        return 0;
    }
    const int mod=1000000007;
    long long a=1;
    for(int i=1;i<=r;i++){
        a*=i;
        a%=mod;
    }
    long long b=a;
    a=1;
    for(int i=mod-2;i;i/=2){
        if(i%2){
            a*=b;
            a%=mod;
        }
        b*=b;
        b%=mod;
    }
    for(int i=n;i>n-r;i--){
        a*=i;
        a%=mod;
    }
    cout<<a<<endl;
    return 0;
}
```