#include <iostream>
#include <algorithm>
#include <functional>
#include <vector>
#include <cassert>
#define rep(i, n) for(i = 0; i < n; i++)
using namespace std;

int n, k;
int st[100000];
int mid[100000];
int ed[100000];

int main() {
	int i;
	
	cin >> n >> k;
	if (k > (n + 1) / 2) { cout << -1 << endl; return 0; }
	
	int num = k;
	
	rep(i, n) { st[i] = num; num++; }
	
	rep(i, n - (2 * k - 1)) { mid[i] = num; num++; }
	for (i = n - (2 * k - 1) + k; i < n; i++) {
		mid[i] = num; num++;
	}
	for (i = n - (2 * k - 1); i < n - (2 * k - 1) + k; i++) {
		mid[i] = num; num++;
	}
	
	typedef pair<int, int> P;	//(val, pos)
	vector<P> vec;
	
	rep(i, n) {
		int lower = st[i] + mid[i];
		vec.push_back(P(lower, i));
	}
	sort(vec.begin(), vec.end(), greater<P>());
	
	num = k + 3 * n - 1;
	rep(i, vec.size()) {
		int pos = vec[i].second;
		if (st[pos] + mid[pos] > num) { assert(0); return 0; }
		ed[pos] = num; num--;
	}
	
	rep(i, n) {
		cout << st[i] << " " << mid[i] << " " << ed[i] << endl;
	}
	return 0;
}
### Prompt

Please create a solution in Cpp 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 <algorithm>
#include <functional>
#include <vector>
#include <cassert>
#define rep(i, n) for(i = 0; i < n; i++)
using namespace std;

int n, k;
int st[100000];
int mid[100000];
int ed[100000];

int main() {
	int i;
	
	cin >> n >> k;
	if (k > (n + 1) / 2) { cout << -1 << endl; return 0; }
	
	int num = k;
	
	rep(i, n) { st[i] = num; num++; }
	
	rep(i, n - (2 * k - 1)) { mid[i] = num; num++; }
	for (i = n - (2 * k - 1) + k; i < n; i++) {
		mid[i] = num; num++;
	}
	for (i = n - (2 * k - 1); i < n - (2 * k - 1) + k; i++) {
		mid[i] = num; num++;
	}
	
	typedef pair<int, int> P;	//(val, pos)
	vector<P> vec;
	
	rep(i, n) {
		int lower = st[i] + mid[i];
		vec.push_back(P(lower, i));
	}
	sort(vec.begin(), vec.end(), greater<P>());
	
	num = k + 3 * n - 1;
	rep(i, vec.size()) {
		int pos = vec[i].second;
		if (st[pos] + mid[pos] > num) { assert(0); return 0; }
		ed[pos] = num; num--;
	}
	
	rep(i, n) {
		cout << st[i] << " " << mid[i] << " " << ed[i] << endl;
	}
	return 0;
}
```