#include <iostream>
using namespace std;
typedef long long ll;
ll n,m,MOD=1e9+7,a,b,ans,bik[1000001];
ll f(ll x,ll y){
    if(y==0)return 1;
    if(y%2==0)return f(x,y/2)*f(x,y/2)%MOD;
    return x*f(x,y-1)%MOD;
}
ll comb(ll x, ll y){
    return bik[x]*f(bik[x-y],MOD-2)%MOD*f(bik[y],MOD-2)%MOD;
}
int main(void){
    cin>>n>>m;
    bik[0]=1;
    for(ll i=1;i<=1000000;i++){
        bik[i]=bik[i-1]*i;
        bik[i]%=MOD;
    }
    a=n+m;
    if(a%3!=0){
        cout<<0<<endl;
        return 0;
    }
    n-=a/3;
    m-=a/3;
    //cout<<n<<" "<<m<<endl;
    if(n>=0&&m>=0){
        cout<<comb(n+m,m)<<endl;
    }
    else cout<<0<<endl;
}

### 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>
using namespace std;
typedef long long ll;
ll n,m,MOD=1e9+7,a,b,ans,bik[1000001];
ll f(ll x,ll y){
    if(y==0)return 1;
    if(y%2==0)return f(x,y/2)*f(x,y/2)%MOD;
    return x*f(x,y-1)%MOD;
}
ll comb(ll x, ll y){
    return bik[x]*f(bik[x-y],MOD-2)%MOD*f(bik[y],MOD-2)%MOD;
}
int main(void){
    cin>>n>>m;
    bik[0]=1;
    for(ll i=1;i<=1000000;i++){
        bik[i]=bik[i-1]*i;
        bik[i]%=MOD;
    }
    a=n+m;
    if(a%3!=0){
        cout<<0<<endl;
        return 0;
    }
    n-=a/3;
    m-=a/3;
    //cout<<n<<" "<<m<<endl;
    if(n>=0&&m>=0){
        cout<<comb(n+m,m)<<endl;
    }
    else cout<<0<<endl;
}

```