#include <bits/stdc++.h>
using namespace std;
typedef int64_t LL;
const int MOD=1e9+7;
const int MAX=1e6;
vector<LL> NMR(MAX),DNM(MAX),INV(MAX);
LL BNM(int n,int k)
{
  if(n<k)return 0;
  if(n<0||k<0)return 0;
  k=min(k,n-k);
  NMR.at(0)=NMR.at(1)=1;
  DNM.at(0)=DNM.at(1)=1;
  INV.at(0)=INV.at(1)=1;
  for(int i=2;i<MAX;i++)
  {
    NMR.at(i)=NMR.at(i-1)*i%MOD;
    INV.at(i)=MOD-INV.at(MOD%i)*(MOD/i)%MOD;
    DNM.at(i)=DNM.at(i-1)*INV.at(i)%MOD;
  }
  return NMR.at(n)*(DNM.at(k)*DNM.at(n-k)%MOD)%MOD;
}
int main()
{
  int x,y,z;
  cin>>x>>y;
  if((x+y)%3>0){cout<<0<<endl;return 0;}
  z=(x+y)/3;
  x-=z;
  y-=z;
  if(x<0||y<0){cout<<0<<endl;return 0;}
  cout<<BNM(x+y,x)<<endl;
}
### 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>
using namespace std;
typedef int64_t LL;
const int MOD=1e9+7;
const int MAX=1e6;
vector<LL> NMR(MAX),DNM(MAX),INV(MAX);
LL BNM(int n,int k)
{
  if(n<k)return 0;
  if(n<0||k<0)return 0;
  k=min(k,n-k);
  NMR.at(0)=NMR.at(1)=1;
  DNM.at(0)=DNM.at(1)=1;
  INV.at(0)=INV.at(1)=1;
  for(int i=2;i<MAX;i++)
  {
    NMR.at(i)=NMR.at(i-1)*i%MOD;
    INV.at(i)=MOD-INV.at(MOD%i)*(MOD/i)%MOD;
    DNM.at(i)=DNM.at(i-1)*INV.at(i)%MOD;
  }
  return NMR.at(n)*(DNM.at(k)*DNM.at(n-k)%MOD)%MOD;
}
int main()
{
  int x,y,z;
  cin>>x>>y;
  if((x+y)%3>0){cout<<0<<endl;return 0;}
  z=(x+y)/3;
  x-=z;
  y-=z;
  if(x<0||y<0){cout<<0<<endl;return 0;}
  cout<<BNM(x+y,x)<<endl;
}
```