#include <bits/stdc++.h>
#include <random>
using namespace std;
using ll = long long;
using ld = long double;
ll Q=1000000007;
const double PI=3.14159265358979323846;

int main(){
  ll X,Y;
  cin >> X >> Y;
  if((X+Y)%3!=0){
    cout << 0 << endl;
    return 0;
  }else if(Y>2*X||X>2*Y){
    cout << 0 << endl;
    return 0;
  }
  ll N=(X+Y)/3;
  ll M=2*N - X;
  // answer is nCm % Q
  vector<ll> inv(N+1,0);
  inv[1]=1;
  for(int i=2;i<=N;i++){
    inv[i]=Q-(Q/i)*inv[Q%i]%Q;
  }
  ll ans = 1;
  for(int i=1;i<=M;i++){
    ans = (ans *((N-i+1)*inv[i]%Q))%Q;
  }
  cout << ans%Q << endl;
}
### 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>
#include <random>
using namespace std;
using ll = long long;
using ld = long double;
ll Q=1000000007;
const double PI=3.14159265358979323846;

int main(){
  ll X,Y;
  cin >> X >> Y;
  if((X+Y)%3!=0){
    cout << 0 << endl;
    return 0;
  }else if(Y>2*X||X>2*Y){
    cout << 0 << endl;
    return 0;
  }
  ll N=(X+Y)/3;
  ll M=2*N - X;
  // answer is nCm % Q
  vector<ll> inv(N+1,0);
  inv[1]=1;
  for(int i=2;i<=N;i++){
    inv[i]=Q-(Q/i)*inv[Q%i]%Q;
  }
  ll ans = 1;
  for(int i=1;i<=M;i++){
    ans = (ans *((N-i+1)*inv[i]%Q))%Q;
  }
  cout << ans%Q << endl;
}
```