#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define all(x) (x).begin(),(x).end()
const int mod=1000000007,MAX=200003,INF=1<<30;

ll rui(ll a,ll b){
    ll ans=1;
    while(b>0){
        if(b&1) ans=ans*a%mod;
        a=a*a%mod;
        b/=2;
    }
    return ans;
}

ll comb(ll a,ll b){
    ll ans=1;
    for(ll i=a;i>a-b;i--){
        ans=ans*i%mod;
    }
    for(ll i=1;i<=b;i++){
        ans=(ans*rui(i,mod-2))%mod;
    }
    return ans;
}


int main(){
    
    int X,Y;cin>>X>>Y;
    if((X+Y)%3!=0) cout<<0<<endl;
    else{
        int A=(X+Y)/3;
        X-=A;Y-=A;
        if(X<0||Y<0) cout<<0<<endl;
        else{
            cout<<comb(A,X)<<endl;
        }
    }
}



### Prompt

Please provide a Cpp coded solution to the problem described below:

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 ll;
#define all(x) (x).begin(),(x).end()
const int mod=1000000007,MAX=200003,INF=1<<30;

ll rui(ll a,ll b){
    ll ans=1;
    while(b>0){
        if(b&1) ans=ans*a%mod;
        a=a*a%mod;
        b/=2;
    }
    return ans;
}

ll comb(ll a,ll b){
    ll ans=1;
    for(ll i=a;i>a-b;i--){
        ans=ans*i%mod;
    }
    for(ll i=1;i<=b;i++){
        ans=(ans*rui(i,mod-2))%mod;
    }
    return ans;
}


int main(){
    
    int X,Y;cin>>X>>Y;
    if((X+Y)%3!=0) cout<<0<<endl;
    else{
        int A=(X+Y)/3;
        X-=A;Y-=A;
        if(X<0||Y<0) cout<<0<<endl;
        else{
            cout<<comb(A,X)<<endl;
        }
    }
}



```