#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll ans=0;
const ll mod=1e9+7;
ll ksm(ll a,ll n)
{
    a%=mod;
    ll ans=1,base=a;
    while(n)
    {
        if(n&1)
            ans=(ans*base)%mod;
        base=(base*base)%mod;
        n>>=1;
    }
    return ans%mod;
}
ll fa(int x)
{
    ll sum=1;
    for(int i=2;i<=x;i++)
        sum=(sum*i)%mod;
    return sum;
}
ll C(ll a,ll b)
{
    return fa(b)*ksm(fa(a)*fa(b-a),mod-2)%mod;
}
int main()
{
    int x,y;
    scanf("%d%d",&x,&y);
    int a=(2*y-x)/3;
    int b=(2*x-y)/3;
    if((x+y)%3==0&&x*2>=y&&y*2>=x)
        printf("%lld\n",C(a,a+b));
    else printf("0\n");
    return 0;
}

### Prompt

Generate 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>
using namespace std;
typedef long long ll;
ll ans=0;
const ll mod=1e9+7;
ll ksm(ll a,ll n)
{
    a%=mod;
    ll ans=1,base=a;
    while(n)
    {
        if(n&1)
            ans=(ans*base)%mod;
        base=(base*base)%mod;
        n>>=1;
    }
    return ans%mod;
}
ll fa(int x)
{
    ll sum=1;
    for(int i=2;i<=x;i++)
        sum=(sum*i)%mod;
    return sum;
}
ll C(ll a,ll b)
{
    return fa(b)*ksm(fa(a)*fa(b-a),mod-2)%mod;
}
int main()
{
    int x,y;
    scanf("%d%d",&x,&y);
    int a=(2*y-x)/3;
    int b=(2*x-y)/3;
    if((x+y)%3==0&&x*2>=y&&y*2>=x)
        printf("%lld\n",C(a,a+b));
    else printf("0\n");
    return 0;
}

```