#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <iomanip>
#include <stack>
#include <set>
#include <map>
#include <list>

using namespace std;

typedef long long int ll;
typedef pair<int, int> Pii;

const ll mod = 998244353;
const ll inf = (ll) 1e18;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  int n, k;
  cin >> n >> k;

  if (n < (k - 1) * 2 + 1) {
    cout << -1 << endl; // impossible
    return 0;
  }

  vector<vector<int> > ans(n, vector<int>(3));
  int ap, bp, cp, pp;
  ap = n/2;
  bp = 0;
  cp = 0;
  pp = 0;
  while (ap < n) {
    ans[pp][0] = k + ap;
    ans[pp][1] = k + bp + n;
    ans[pp][2] = k + cp + n * 2;
    ap++;
    bp++;
    cp += 2;
    pp++;
  }
  ap = 0;
  cp = 1;
  while (cp < n) {
    ans[pp][0] = k + ap;
    ans[pp][1] = k + bp + n;
    ans[pp][2] = k + cp + n * 2;
    ap++;
    bp++;
    cp += 2;
    pp++;
  }

  for (auto &x: ans) {
    cout << x[0] << " " << x[1] << " " << x[2] << endl;
  }

  return 0;
}

### Prompt

Your task is to create 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 <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <iomanip>
#include <stack>
#include <set>
#include <map>
#include <list>

using namespace std;

typedef long long int ll;
typedef pair<int, int> Pii;

const ll mod = 998244353;
const ll inf = (ll) 1e18;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  int n, k;
  cin >> n >> k;

  if (n < (k - 1) * 2 + 1) {
    cout << -1 << endl; // impossible
    return 0;
  }

  vector<vector<int> > ans(n, vector<int>(3));
  int ap, bp, cp, pp;
  ap = n/2;
  bp = 0;
  cp = 0;
  pp = 0;
  while (ap < n) {
    ans[pp][0] = k + ap;
    ans[pp][1] = k + bp + n;
    ans[pp][2] = k + cp + n * 2;
    ap++;
    bp++;
    cp += 2;
    pp++;
  }
  ap = 0;
  cp = 1;
  while (cp < n) {
    ans[pp][0] = k + ap;
    ans[pp][1] = k + bp + n;
    ans[pp][2] = k + cp + n * 2;
    ap++;
    bp++;
    cp += 2;
    pp++;
  }

  for (auto &x: ans) {
    cout << x[0] << " " << x[1] << " " << x[2] << endl;
  }

  return 0;
}

```