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

long long X,Y;long long base=1000000007LL;

long long kaijo(long long a) {
  if (a==0) return 1LL;
  else {
    return a*kaijo(a-1)%base;
  }
}

long long ruijo(long long a,long long b) {
  if (b==0LL) return 1LL;
  else {
    if (b%2==0) return (ruijo(a,b/2)*ruijo(a,b/2))%base;
    else return (a*ruijo(a,b-1))%base;
  }
}

int main() {
  cin >> X >> Y;
  if ((X+Y)%3LL!=0LL || Y>2*X || X>2*Y) cout << 0 << endl;
  else {
    long long k=(X+Y)/3LL;
    long long x=(2*Y-X)/3LL;
    long long y=(2*X-Y)/3LL;
    long long a=(kaijo(x)*kaijo(y))%base;
    cout << (kaijo(k)*ruijo(a,base-2LL))%base << endl;
  }
}
### Prompt

Your challenge is to write 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;

long long X,Y;long long base=1000000007LL;

long long kaijo(long long a) {
  if (a==0) return 1LL;
  else {
    return a*kaijo(a-1)%base;
  }
}

long long ruijo(long long a,long long b) {
  if (b==0LL) return 1LL;
  else {
    if (b%2==0) return (ruijo(a,b/2)*ruijo(a,b/2))%base;
    else return (a*ruijo(a,b-1))%base;
  }
}

int main() {
  cin >> X >> Y;
  if ((X+Y)%3LL!=0LL || Y>2*X || X>2*Y) cout << 0 << endl;
  else {
    long long k=(X+Y)/3LL;
    long long x=(2*Y-X)/3LL;
    long long y=(2*X-Y)/3LL;
    long long a=(kaijo(x)*kaijo(y))%base;
    cout << (kaijo(k)*ruijo(a,base-2LL))%base << endl;
  }
}
```