#include<bits/stdc++.h>
using namespace std;
typedef long long int ll;
ll p[1000005],hell=pow(10,9)+7;
ll exp(ll x,ll y){
    ll res=1;
    while(y>0){
        if(y&1)
        res=(res*x)%hell;
        y>>=1;
        x=(x*x)%hell;
    }
    return res;
}
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    p[0]=1;
    for(ll i=1;i<1000005;i++)
    p[i]=(i*p[i-1])%hell;
    ll x,y;
    cin>>x>>y;
    ll x0=(2*x-y)/3,y0=(2*y-x)/3;
    if(((2*x-y)%3)||((2*y-x)%3)||x0<0||y0<0){
        cout<<0;
        exit(0);
    }
    ll res=p[x0+y0];
    res*=exp(p[x0],hell-2);
    res%=hell;
    res*=exp(p[y0],hell-2);
    res%=hell;
    cout<<res;
}
### Prompt

Generate 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;
typedef long long int ll;
ll p[1000005],hell=pow(10,9)+7;
ll exp(ll x,ll y){
    ll res=1;
    while(y>0){
        if(y&1)
        res=(res*x)%hell;
        y>>=1;
        x=(x*x)%hell;
    }
    return res;
}
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    p[0]=1;
    for(ll i=1;i<1000005;i++)
    p[i]=(i*p[i-1])%hell;
    ll x,y;
    cin>>x>>y;
    ll x0=(2*x-y)/3,y0=(2*y-x)/3;
    if(((2*x-y)%3)||((2*y-x)%3)||x0<0||y0<0){
        cout<<0;
        exit(0);
    }
    ll res=p[x0+y0];
    res*=exp(p[x0],hell-2);
    res%=hell;
    res*=exp(p[y0],hell-2);
    res%=hell;
    cout<<res;
}
```