#include<iostream>
#include<cmath>
#define MOD 1000000007

using namespace std;

long long power(long long a,long long x){
    return x?x%2?power(a,x-1)*a%MOD:(long long)powl(power(a,x/2),2)%MOD:1;
}
long long nCr(long long n,long long r){
    long long nCr=1LL;
    for(long long i=n;i>n-r;nCr%=MOD,i--)nCr*=i;
    for(long long i=1;i<=r;nCr%=MOD,i++)nCr*=power(i,MOD-2);
    return nCr;
}


int main(){
    long long x,y;
    cin>>x>>y;
    long long r=(2*y-x)/3LL,n=r+(y-2*r);
    if((2*y-x)%3!=0LL||r<0||n<=0){cout<<0<<endl;return 0;}

    cout<<nCr(n,r)<<endl;

    return 0;
}
### 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<iostream>
#include<cmath>
#define MOD 1000000007

using namespace std;

long long power(long long a,long long x){
    return x?x%2?power(a,x-1)*a%MOD:(long long)powl(power(a,x/2),2)%MOD:1;
}
long long nCr(long long n,long long r){
    long long nCr=1LL;
    for(long long i=n;i>n-r;nCr%=MOD,i--)nCr*=i;
    for(long long i=1;i<=r;nCr%=MOD,i++)nCr*=power(i,MOD-2);
    return nCr;
}


int main(){
    long long x,y;
    cin>>x>>y;
    long long r=(2*y-x)/3LL,n=r+(y-2*r);
    if((2*y-x)%3!=0LL||r<0||n<=0){cout<<0<<endl;return 0;}

    cout<<nCr(n,r)<<endl;

    return 0;
}
```