Problem:
Score : 700 points

Problem Statement

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

Sample Input 1

1 1

Sample Output 1

1 2 3

Sample Input 2

3 3

Sample Output 2

-1

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define MOD (ll)(1e9 + 7)
#define MAX (ll)(2e5 + 4)
#define INF (ll)(1e17)
using namespace std;
using ll =  long long;
using ld = long double;

int main () {
	int n, k;
	cin >> n >> k;
	int a = k, b = 2 * n;
	set<int> sa, sb, sc;
	int aa = 0, bb = 0;
	for (int i = 1; i <= n; i++) {
		sa.insert (k + i - 1);
		sb.insert (k + i - 1 + n);
		sc.insert (k + i - 1 + 2 * n);	
	}
	if (k * 2 > n + 1) {
		cout << "-1\n";	
		return 0;
	}
	while (a + b < k + 3 * n && b < k + 2 * n && a < k + n) {
		sa.erase (a), sb.erase (b), sc.erase (a + b);
		cout << a << " " << b << " " << a + b << "\n";
		a++, b++;
	}
	while (sa.size ()) {
		sa.erase (sa.begin ());
		sb.erase (sb.begin ());
		sc.erase (sc.begin ());
	}
}