#include <bits/stdc++.h>
using namespace std;
long long INF=1e9+7;
long long modinv(long long a, long long m) {
    long long b = m, u = 1, v = 0;
    while (b) {
        long long t = a / b;
        a -= t * b; swap(a, b);
        u -= t * v; swap(u, v);
    }
    u %= m;
    if (u < 0) u += m;
    return u;
}
#define int long long
signed main(){
  int a,b; cin>>a>>b;
  if((a+b)%3!=0||a*2<b||b*2<a){cout<<0<<endl;return 0;}
  int c=((a+b)/3-(a-b))/2,d=(a+b)/3-c;
  int count=1;
  for(int i=c+d;i>d;i--){
    count*=i;
    count%=INF;
  }
  int A=1;
  for(int i=1;i<=c;i++){
    A*=i;
    A%=INF;
  }
  int B=modinv(A,INF);
  count*=B;
  count%=INF;
  cout<<count<<endl;
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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 INF=1e9+7;
long long modinv(long long a, long long m) {
    long long b = m, u = 1, v = 0;
    while (b) {
        long long t = a / b;
        a -= t * b; swap(a, b);
        u -= t * v; swap(u, v);
    }
    u %= m;
    if (u < 0) u += m;
    return u;
}
#define int long long
signed main(){
  int a,b; cin>>a>>b;
  if((a+b)%3!=0||a*2<b||b*2<a){cout<<0<<endl;return 0;}
  int c=((a+b)/3-(a-b))/2,d=(a+b)/3-c;
  int count=1;
  for(int i=c+d;i>d;i--){
    count*=i;
    count%=INF;
  }
  int A=1;
  for(int i=1;i<=c;i++){
    A*=i;
    A%=INF;
  }
  int B=modinv(A,INF);
  count*=B;
  count%=INF;
  cout<<count<<endl;
}
```