#include<bits/stdc++.h>
typedef long long ll;
const ll mod=1e9+7;
using namespace std;
ll ksm(ll a,ll b)
{
    ll ans=1;
    for(;b;b>>=1,a=a*a%mod) if(b&1) ans=ans*a%mod;
    return ans;
}
ll C(ll a,ll b)
{
    ll s1=1,s2=1;
    for(ll i=1;i<=b;i++) s2=s2*i%mod;
    for(ll i=a-b+1;i<=a;i++) s1=s1*i%mod;
    return s1*ksm(s2,mod-2)%mod;
}
int main()
{
    int x,y;cin>>x>>y;
    if((2*y-x)%3==0&&(2*y)-x>=0)
    {
        int a=(2*y-x)/3;
        int b=(2*x-y)/3;
        cout<<C(a+b,a)<<endl;
    }
    else
        cout<<0<<endl;
    return 0;
}

### 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>
typedef long long ll;
const ll mod=1e9+7;
using namespace std;
ll ksm(ll a,ll b)
{
    ll ans=1;
    for(;b;b>>=1,a=a*a%mod) if(b&1) ans=ans*a%mod;
    return ans;
}
ll C(ll a,ll b)
{
    ll s1=1,s2=1;
    for(ll i=1;i<=b;i++) s2=s2*i%mod;
    for(ll i=a-b+1;i<=a;i++) s1=s1*i%mod;
    return s1*ksm(s2,mod-2)%mod;
}
int main()
{
    int x,y;cin>>x>>y;
    if((2*y-x)%3==0&&(2*y)-x>=0)
    {
        int a=(2*y-x)/3;
        int b=(2*x-y)/3;
        cout<<C(a+b,a)<<endl;
    }
    else
        cout<<0<<endl;
    return 0;
}

```