#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int M=1000000007;
const int N=2000100;

ll pwr(ll a, ll e){
  if(e==0)return 1;
  if(e%2==1)return a*pwr(a,e-1)%M;
  ll h=pwr(a,e/2);
  return h*h%M;
}

ll inv(ll a){return pwr(a,M-2);}

ll f[N+1];
ll fi[N+1];

ll C(ll n, ll k){
if(n<0||k<0) return 0;
  return f[n]*fi[k]%M*fi[n-k]%M;
}

int main(){
  f[0]=1;
  for(int i=1;i<=N;i++)
    f[i]=f[i-1]*i%M;
  for(int i=0;i<=N;i++)
    fi[i]=inv(f[i]);
int x,y;
  cin>>x>>y;
  ll a=2*x-y;
  ll b=2*y-x;
  if(a%3!=0||b%3!=0||a<0||b<0){
    cout<<0;
  }else{
    a/=3;
    b/=3;
    cout <<C(a+b,a);
  }
}

### 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;
const int M=1000000007;
const int N=2000100;

ll pwr(ll a, ll e){
  if(e==0)return 1;
  if(e%2==1)return a*pwr(a,e-1)%M;
  ll h=pwr(a,e/2);
  return h*h%M;
}

ll inv(ll a){return pwr(a,M-2);}

ll f[N+1];
ll fi[N+1];

ll C(ll n, ll k){
if(n<0||k<0) return 0;
  return f[n]*fi[k]%M*fi[n-k]%M;
}

int main(){
  f[0]=1;
  for(int i=1;i<=N;i++)
    f[i]=f[i-1]*i%M;
  for(int i=0;i<=N;i++)
    fi[i]=inv(f[i]);
int x,y;
  cin>>x>>y;
  ll a=2*x-y;
  ll b=2*y-x;
  if(a%3!=0||b%3!=0||a<0||b<0){
    cout<<0;
  }else{
    a/=3;
    b/=3;
    cout <<C(a+b,a);
  }
}

```