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

### Prompt

Your challenge is to write 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>
typedef long long ll;
using namespace std;
ll a,b,m,n,MOD=1e9+7;
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 f(x,y-1)*x%MOD;
}
ll bik(ll x){
    ll l=1;
    for(int i=1;i<=x;i++){
        l*=i;
        l%=MOD;
    }
    return l;
}
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>>a>>b;
    if((2*a-b)%3==0&&(2*b-a)%3==0&&2*a-b>=0&&2*b-a>=0){
        m=(2*a-b)/3,n=(2*b-a)/3;
        cout<<comb(m+n,m)<<endl;
    }
    else cout<<0<<endl;
}

```