#include <iostream>
#include <string>
#include <algorithm>
#include <cmath>
#include <functional>
#include <vector>
#include <queue>
#include <deque>
#include <map>
#include <set>
#define nmax_def 110000
#define Cmax_def 2200
#define mod 1000000007
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;

int main() {
	ll N, K;
	cin >> N >> K;
	if (2 * K > 1 + N) {
		cout << "-1" << endl;
	}
	else {
		ll N_2 = N / 2;
		rep(i, N) {
			ll a = K;
			ll b = K + N;
			ll c = K + N * 2;
			if (i < N_2) {
				a += N_2 - 1 - i;
				b += 2 * i + 1;
			}
			else {
				a += N + N_2 - 1 - i;
				b += 2 * (i - N_2);
			}
			c += i;
			cout << a << " " << b << " " << c << endl;
		}
	}

	return 0;
}
### Prompt

Construct a CPP code solution to the problem outlined:

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 <string>
#include <algorithm>
#include <cmath>
#include <functional>
#include <vector>
#include <queue>
#include <deque>
#include <map>
#include <set>
#define nmax_def 110000
#define Cmax_def 2200
#define mod 1000000007
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;

int main() {
	ll N, K;
	cin >> N >> K;
	if (2 * K > 1 + N) {
		cout << "-1" << endl;
	}
	else {
		ll N_2 = N / 2;
		rep(i, N) {
			ll a = K;
			ll b = K + N;
			ll c = K + N * 2;
			if (i < N_2) {
				a += N_2 - 1 - i;
				b += 2 * i + 1;
			}
			else {
				a += N + N_2 - 1 - i;
				b += 2 * (i - N_2);
			}
			c += i;
			cout << a << " " << b << " " << c << endl;
		}
	}

	return 0;
}
```