#include <bits/stdc++.h>
#define ll long long
#define x first
#define y second
using namespace std;
typedef pair <int,int> ii;
const ll MOD=1e9+7;
ll luythua(ll x,int y){
    if(y==0)return 1;
    ll k=luythua(x,y/2);
    return k*k%MOD*(y%2?x:1)%MOD;
}
ll C(int n,int k){
    if(n-k<k)k=n-k;
    ll res=1;
    for(int i=0;i<k;i++){
        res=res*(n-i)%MOD;
        res=res*luythua(i+1,MOD-2)%MOD;
    }
    return res;
}
int main() {
    int x,y;
    cin >> x >> y;
    if ((x+y)%3!=0||min(x,y)*2<max(x,y)) cout << 0;
    else {
        int k=abs(x-y);
        int bao = (x+y)/3;
        int hung=(bao-k)/2;
        cout<<C(bao,hung);
    }
}

### 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>
#define ll long long
#define x first
#define y second
using namespace std;
typedef pair <int,int> ii;
const ll MOD=1e9+7;
ll luythua(ll x,int y){
    if(y==0)return 1;
    ll k=luythua(x,y/2);
    return k*k%MOD*(y%2?x:1)%MOD;
}
ll C(int n,int k){
    if(n-k<k)k=n-k;
    ll res=1;
    for(int i=0;i<k;i++){
        res=res*(n-i)%MOD;
        res=res*luythua(i+1,MOD-2)%MOD;
    }
    return res;
}
int main() {
    int x,y;
    cin >> x >> y;
    if ((x+y)%3!=0||min(x,y)*2<max(x,y)) cout << 0;
    else {
        int k=abs(x-y);
        int bao = (x+y)/3;
        int hung=(bao-k)/2;
        cout<<C(bao,hung);
    }
}

```