#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

int mod=1e9+7;

int mpow(ll a,ll b) {
    ll c=1;
    while (b) {
        if (b%2) c=c*a%mod;
        b/=2;
        a=a*a%mod;
    }
    return c;
}

int C(ll a,ll b) {
    ll nume=1;
    for (int i=a;i>a-b;i--)
        nume=nume*i%mod;
    ll deno=1;
    for (int i=2;i<=b;i++)
        deno=deno*i%mod;
    return nume*mpow(deno,mod-2)%mod;
}

int main() {
    int x,y;cin>>x>>y;
    int a=(x+y)/3;
    int b=x-a;
    int c=y-a;
    if ((x+y)%3!=0||b<0||c<0) {
        cout<<0<<endl;
        return 0;
    }
    cout<<C(b+c,b)<<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>
using namespace std;
typedef long long ll;

int mod=1e9+7;

int mpow(ll a,ll b) {
    ll c=1;
    while (b) {
        if (b%2) c=c*a%mod;
        b/=2;
        a=a*a%mod;
    }
    return c;
}

int C(ll a,ll b) {
    ll nume=1;
    for (int i=a;i>a-b;i--)
        nume=nume*i%mod;
    ll deno=1;
    for (int i=2;i<=b;i++)
        deno=deno*i%mod;
    return nume*mpow(deno,mod-2)%mod;
}

int main() {
    int x,y;cin>>x>>y;
    int a=(x+y)/3;
    int b=x-a;
    int c=y-a;
    if ((x+y)%3!=0||b<0||c<0) {
        cout<<0<<endl;
        return 0;
    }
    cout<<C(b+c,b)<<endl;
    return 0;
}
```