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

int main() {
  long n, k;
  cin >> n >> k;
  if (2 * k > n + 1) {
    cout << -1 << endl;
    return 0;
  }
  int nhalf = n / 2;
  for (int i = 0; i < n; i++) {
    if (i % 2 == 0) {
      cout << k + i / 2 << " " << k + n + nhalf + i / 2 << " " <<
        k + 2 * n + i << "\n";
    } else {
      cout << k + n - nhalf + i / 2 << " " << k + n + i / 2 << " " <<
        k + 2 * n + i << "\n";
    }
  }
}

### Prompt

Generate a cpp solution to the following problem:

Given are positive integers N and K.

Determine if the 3N integers K, K+1, ..., K+3N-1 can be partitioned into N triples (a_1,b_1,c_1), ..., (a_N,b_N,c_N) so that the condition below is satisfied. Any of the integers K, K+1, ..., K+3N-1 must appear in exactly one of those triples.

* For every integer i from 1 to N, a_i + b_i \leq c_i holds.



If the answer is yes, construct one such partition.

Constraints

* 1 \leq N \leq 10^5
* 1 \leq K \leq 10^9

Input

Input is given from Standard Input in the following format:


N K


Output

If it is impossible to partition the integers satisfying the condition, print `-1`. If it is possible, print N triples in the following format:


a_1 b_1 c_1
:
a_N b_N c_N

Output

If it is impossible to partition the integers satisfying the condition, print `-1`. If it is possible, print N triples in the following format:


a_1 b_1 c_1
:
a_N b_N c_N

Examples

Input

1 1


Output

1 2 3


Input

3 3


Output

-1

### Response

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

int main() {
  long n, k;
  cin >> n >> k;
  if (2 * k > n + 1) {
    cout << -1 << endl;
    return 0;
  }
  int nhalf = n / 2;
  for (int i = 0; i < n; i++) {
    if (i % 2 == 0) {
      cout << k + i / 2 << " " << k + n + nhalf + i / 2 << " " <<
        k + 2 * n + i << "\n";
    } else {
      cout << k + n - nhalf + i / 2 << " " << k + n + i / 2 << " " <<
        k + 2 * n + i << "\n";
    }
  }
}

```