#include <bits/stdc++.h>
#define ll long long
using namespace std;
const ll mod=1e9+7;
ll x,y;
ll fac[1000050],inv[1000050];
ll mi(ll a,ll b)
{
    ll ret=1;
    while(b)
    {
        if(b&1)ret=ret*a,ret%=mod;
        b>>=1;
        a=a*a,a%=mod;
    }
    return ret;
}

ll C(ll n,ll m)
{
    if(n==m||m==0)return 1LL;
    return fac[n]*inv[m]%mod*inv[n-m]%mod;
}

int main()
{
    fac[0]=1;
    for(int i=1;i<=1000000;++i)fac[i]=fac[i-1]*i%mod;
    for(int i=1;i<=1000000;++i)inv[i]=mi(fac[i],mod-2);
    cin>>x>>y;
    ll s=x+y;
    if(s%3>0||abs(x-y)>s/3)return puts("0"),0;
    int cnt=0;
    ll ans=0;
    ll n=s/3;
    ll m=abs(x-n*2);
    ans=C(n,m);
    cout<<ans<<endl;
    return 0;
}

### 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 <bits/stdc++.h>
#define ll long long
using namespace std;
const ll mod=1e9+7;
ll x,y;
ll fac[1000050],inv[1000050];
ll mi(ll a,ll b)
{
    ll ret=1;
    while(b)
    {
        if(b&1)ret=ret*a,ret%=mod;
        b>>=1;
        a=a*a,a%=mod;
    }
    return ret;
}

ll C(ll n,ll m)
{
    if(n==m||m==0)return 1LL;
    return fac[n]*inv[m]%mod*inv[n-m]%mod;
}

int main()
{
    fac[0]=1;
    for(int i=1;i<=1000000;++i)fac[i]=fac[i-1]*i%mod;
    for(int i=1;i<=1000000;++i)inv[i]=mi(fac[i],mod-2);
    cin>>x>>y;
    ll s=x+y;
    if(s%3>0||abs(x-y)>s/3)return puts("0"),0;
    int cnt=0;
    ll ans=0;
    ll n=s/3;
    ll m=abs(x-n*2);
    ans=C(n,m);
    cout<<ans<<endl;
    return 0;
}

```