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 r(i,n) for(int i=0;i<n;i++)
#define int long long
using namespace std;
typedef pair<int,int>P;
typedef pair<P,int>P2;
#define F first
#define S second

signed main(){
	vector<P2>v;
	int n,k;
	cin>>n>>k;
	//cout<<endl;
for(int ppp=0;ppp<5;ppp++){
	set<int>B,C,D;
	r(i,n){
		B.insert(-(k+n+i));
		//cout<<(k+n+i)<<endl;
	}
	//cout<<endl;
	r(i,n){
		C.insert((k+n*2+i));
		D.insert(-(k+n*2+i));
		//cout<<((k+n*2+i))<<endl;
	}
	v.clear();

	for(int x=n+k-1-ppp,i=0;i<n;i++,x--){
		if(x==0)x=n+k-1;
		int y=(-(*D.begin()))-x;
		//cout<<(-(*D.begin()))<<' '<<y<<' '<<x<<endl;
		set<int>::iterator it=(B.lower_bound(-y));
		if(it==B.end()){
			goto L;
			return 0;
		}
		int z=-(*it);
		int p=(x+z);
		//cout<<p<<endl;
		set<int>::iterator it2=(C.lower_bound(p));
		if(it2==C.end()){
			goto L;
			return 0;
		}
		int u=(*it2);
		B.erase(-z);
		C.erase(u);
		D.erase(-u);
		v.push_back(P2(P(x,z),u));
	}
	if(0){
		L:;
		if(ppp==4){
			cout<<-1<<endl;
			return 0;
		}
	}
}
	r(i,n){
		cout<<v[i].F.F<<' '<<v[i].F.S<<' '<<v[i].S<<endl;
	}
}