#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <cmath>
#include <map>
#include <numeric>
using namespace std;
typedef long long ll;
typedef long double ld;
ll mod=1e9+7;

ll power(ll a,ll b){
    ll res=1;
    while(b){
        if(b&1)res=res*a %mod;
        a=a*a %mod;
        b/=2;
    }
    return res;
}

ll c(ll a,ll b){
    ll res=1;
    for(ll i=1;i<=b;i++)res=res*(a+1-i)%mod *power(i,mod-2)%mod;
    return res;
}

int main(){
    ll x,y;cin>>x>>y;
    if((x+y)%3!=0){cout<<0;return 0;}
    ll m=(2*x-y)/3,n=(2*y-x)/3;
    if(m<0||n<0){cout<<0;return 0;}
    if(m==0||n==0){cout<<1;return 0;}
    cout<<c(m+n,min(n,m))%mod;
}
### Prompt

Create a solution in CPP for 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>
#include <string>
#include <vector>
#include <algorithm>
#include <cmath>
#include <map>
#include <numeric>
using namespace std;
typedef long long ll;
typedef long double ld;
ll mod=1e9+7;

ll power(ll a,ll b){
    ll res=1;
    while(b){
        if(b&1)res=res*a %mod;
        a=a*a %mod;
        b/=2;
    }
    return res;
}

ll c(ll a,ll b){
    ll res=1;
    for(ll i=1;i<=b;i++)res=res*(a+1-i)%mod *power(i,mod-2)%mod;
    return res;
}

int main(){
    ll x,y;cin>>x>>y;
    if((x+y)%3!=0){cout<<0;return 0;}
    ll m=(2*x-y)/3,n=(2*y-x)/3;
    if(m<0||n<0){cout<<0;return 0;}
    if(m==0||n==0){cout<<1;return 0;}
    cout<<c(m+n,min(n,m))%mod;
}
```