#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;

const int mod=1e9+7;
ll fac[2000010],finv[2000010],inv[2000010];
void init(int n);

int main(void){
  int x,y,m1,m2;
  cin >> x >> y;
  if ((x+y)%3!=0){
    cout << 0 << endl;
    return 0;
  }
  m1=x-(x+y)/3;
  m2=y-(x+y)/3;
  init(m1+m2);
  cout << fac[m1+m2]*(finv[m1]*finv[m2]%mod)%mod << endl;
  return 0;
}

void init(int n){
  fac[0]=fac[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  for (int i=2;i<=n;i++){
    fac[i]=(fac[i-1]*i)%mod;
    inv[i]=mod-(inv[mod%i]*(mod/i))%mod;
    finv[i]=(finv[i-1]*inv[i])%mod;
  }
}
### 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 <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;

const int mod=1e9+7;
ll fac[2000010],finv[2000010],inv[2000010];
void init(int n);

int main(void){
  int x,y,m1,m2;
  cin >> x >> y;
  if ((x+y)%3!=0){
    cout << 0 << endl;
    return 0;
  }
  m1=x-(x+y)/3;
  m2=y-(x+y)/3;
  init(m1+m2);
  cout << fac[m1+m2]*(finv[m1]*finv[m2]%mod)%mod << endl;
  return 0;
}

void init(int n){
  fac[0]=fac[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  for (int i=2;i<=n;i++){
    fac[i]=(fac[i-1]*i)%mod;
    inv[i]=mod-(inv[mod%i]*(mod/i))%mod;
    finv[i]=(finv[i-1]*inv[i])%mod;
  }
}
```