#include<bits/stdc++.h>
using namespace std;
int x,y;
const int N=1e6+9;
const int mod=1e9+7;
int inv[N],frac[N];
void init(){
  frac[0]=frac[1]=inv[0]=inv[1]=1;
  for(int i=2;i<N;i++)frac[i]=1ll*i*frac[i-1]%mod,
  inv[i]=1ll*(mod-mod/i)*inv[mod%i]%mod;
  for(int i=2;i<N;i++)inv[i]=1ll*inv[i]*inv[i-1]%mod;
}
int C(int x,int y){
  return 1ll*frac[x]*inv[x-y]%mod*inv[y]%mod;
}
int main(){
  init();
  cin>>x>>y;
  int t=(x+y)/3;
  int ans=0;
  if(x>=t&&x<=2*t&&((x+y)%3==0))ans=C(t,x-t);
  cout<<ans<<endl;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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;
int x,y;
const int N=1e6+9;
const int mod=1e9+7;
int inv[N],frac[N];
void init(){
  frac[0]=frac[1]=inv[0]=inv[1]=1;
  for(int i=2;i<N;i++)frac[i]=1ll*i*frac[i-1]%mod,
  inv[i]=1ll*(mod-mod/i)*inv[mod%i]%mod;
  for(int i=2;i<N;i++)inv[i]=1ll*inv[i]*inv[i-1]%mod;
}
int C(int x,int y){
  return 1ll*frac[x]*inv[x-y]%mod*inv[y]%mod;
}
int main(){
  init();
  cin>>x>>y;
  int t=(x+y)/3;
  int ans=0;
  if(x>=t&&x<=2*t&&((x+y)%3==0))ans=C(t,x-t);
  cout<<ans<<endl;
}

```