/* In the name of Allah */
#include<bits/stdc++.h>
using namespace std;

int main() {
	int n, k;
	cin >> n >> k;
	if (k + k > n + 1)
		return cout << -1, 0;
	int a = n, b = 3 * n + 2 >> 1, c = 3 * n;
	for ( ; a > 0; a--)
		cout << --a + k << ' ' << b++ + k - 1 << ' ' << --c + k << endl;
	for (a = n - 1, b = n + 1; a > 0; a--)
		cout << --a + k << ' ' << b++ + k - 1 << ' ' << --c + k << endl;
}

### Prompt

In CPP, your task is to solve 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
/* In the name of Allah */
#include<bits/stdc++.h>
using namespace std;

int main() {
	int n, k;
	cin >> n >> k;
	if (k + k > n + 1)
		return cout << -1, 0;
	int a = n, b = 3 * n + 2 >> 1, c = 3 * n;
	for ( ; a > 0; a--)
		cout << --a + k << ' ' << b++ + k - 1 << ' ' << --c + k << endl;
	for (a = n - 1, b = n + 1; a > 0; a--)
		cout << --a + k << ' ' << b++ + k - 1 << ' ' << --c + k << endl;
}

```