#include<bits/stdc++.h>
using namespace std;

const long long MOD = 1000000007;

long long mod_pow(long long x, long long y){
  return y ? mod_pow(x * x % MOD, y / 2) * (y % 2 ? x : 1) % MOD : 1;
}

long long combination(long long n, long long k){
  long long a = 1, b = 1;
  for(int i = n; i > k; --i){
    a = a * i % MOD;
    b = b * (n - i + 1) % MOD;
  }
  return a * mod_pow(b, MOD - 2) % MOD;
}

int main(){
  int x, y;
  cin >> x >> y;
  int xy = x + y;
  if(xy % 3 != 0){
    cout << 0 << endl;
    return 0;
  }
  int n = xy / 3; 
  x -= n;
  y -= n;
  if(x < 0 || y < 0){
    cout << 0 << endl;
    return 0;
  }
  cout << combination(n, x) << endl;
}
### Prompt

Construct a CPP code solution to the problem outlined:

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;

const long long MOD = 1000000007;

long long mod_pow(long long x, long long y){
  return y ? mod_pow(x * x % MOD, y / 2) * (y % 2 ? x : 1) % MOD : 1;
}

long long combination(long long n, long long k){
  long long a = 1, b = 1;
  for(int i = n; i > k; --i){
    a = a * i % MOD;
    b = b * (n - i + 1) % MOD;
  }
  return a * mod_pow(b, MOD - 2) % MOD;
}

int main(){
  int x, y;
  cin >> x >> y;
  int xy = x + y;
  if(xy % 3 != 0){
    cout << 0 << endl;
    return 0;
  }
  int n = xy / 3; 
  x -= n;
  y -= n;
  if(x < 0 || y < 0){
    cout << 0 << endl;
    return 0;
  }
  cout << combination(n, x) << endl;
}
```