#include<bits/stdc++.h>
#define int long long
using namespace std;
constexpr int mod=1e9+7;
int mod_pow(int x,int n){
    if(n==0)
        return 1;
    int res=mod_pow(x*x%mod,n/2);
    if(n%2==1)
        res=res*x%mod;
    return res;
}
int mod_fact(int n){
    return(n==0?1:mod_fact(n-1)*n%mod);
}
int mod_comb(int n,int k){
    int a1=mod_fact(n),a2=mod_fact(k),a3=mod_fact(n-k);
    return a1*mod_pow(a2*a3%mod,mod-2)%mod;
}
signed main(){
    int x,y;
    cin>>x>>y;
    if((2*x-y)%3!=0||(2*y-x)%3!=0||2*x<y||2*y<x){
        cout<<0<<endl;
        return 0;
    }
    cout<<mod_comb((x+y)/3,(2*x-y)/3)<<endl;
}

### Prompt

Your task is to create 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>
#define int long long
using namespace std;
constexpr int mod=1e9+7;
int mod_pow(int x,int n){
    if(n==0)
        return 1;
    int res=mod_pow(x*x%mod,n/2);
    if(n%2==1)
        res=res*x%mod;
    return res;
}
int mod_fact(int n){
    return(n==0?1:mod_fact(n-1)*n%mod);
}
int mod_comb(int n,int k){
    int a1=mod_fact(n),a2=mod_fact(k),a3=mod_fact(n-k);
    return a1*mod_pow(a2*a3%mod,mod-2)%mod;
}
signed main(){
    int x,y;
    cin>>x>>y;
    if((2*x-y)%3!=0||(2*y-x)%3!=0||2*x<y||2*y<x){
        cout<<0<<endl;
        return 0;
    }
    cout<<mod_comb((x+y)/3,(2*x-y)/3)<<endl;
}

```