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

int main() {
	
	ios::sync_with_stdio(0);
	cin.tie(0), cout.tie(0);
	
	int n, k; cin >> n >> k;
	if (k <= (n + 1) / 2) {
		int j = n + (n - 1) / 2, sum = k + 2 * n;
		for (int i = 0; i < n; i += 2) cout << k + i << " " << k + j << " " << sum << "\n", sum++, j--;
		j = n + n - 1;
		for (int i = 1; i < n; i += 2) cout << k + i << " " << k + j << " " << sum << "\n", sum++, j--;
		return 0;
	} else cout << "-1\n";
	
	return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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() {
	
	ios::sync_with_stdio(0);
	cin.tie(0), cout.tie(0);
	
	int n, k; cin >> n >> k;
	if (k <= (n + 1) / 2) {
		int j = n + (n - 1) / 2, sum = k + 2 * n;
		for (int i = 0; i < n; i += 2) cout << k + i << " " << k + j << " " << sum << "\n", sum++, j--;
		j = n + n - 1;
		for (int i = 1; i < n; i += 2) cout << k + i << " " << k + j << " " << sum << "\n", sum++, j--;
		return 0;
	} else cout << "-1\n";
	
	return 0;
}

```