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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Numerics;
using static System.Math;
using static System.Array;
using static AtCoder.IO_ShortCut;
using static AtCoder.Tool;
using static AtCoder.ModInt;
namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        //const int MOD = 998244353;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dI = { 0, 1, 0, -1, 1, -1, -1, 1 };
        static readonly int[] dJ = { 1, 0, -1, 0, 1, 1, -1, -1 };
        static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>> G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }
        static void Solve()
        {
            long N, K;
            Input(out N, out K);
            if (2 * K > N + 1) { OutL(-1);return; }
            if (N % 2 == 1)
            {
                for(var i = 0; i < (N + 1) / 2; i++)
                {
                    Out_Sep(K + (N - 1) / 2 - i, K + 2 * N - 1 - i, K + 3 * N - 1 - 2 * i);
                }
                for(var i = 0; i < N - (N + 1) / 2; i++)
                {
                    Out_Sep(K + N - 1 - i, K + N + (N - 1) / 2 - 1 - i, K + 3 * N - 1 - 1 - 2 * i);
                }
            }
            else
            {
                for(var i = 0; i < N / 2; i++)
                {
                    Out_Sep(K + 2 * N - 1 - i, K + (N / 2 - 1) - i, K + 3 * N - 1 - 2 * i);
                }
                for(var i = 0; i < N / 2; i++)
                {
                    Out_Sep(K + N - 1 - i, K + N + (N / 2 - 1) - i, K + 3 * N - 1 - 1 - 2 * i);
                }
            }
        }
        
        public struct Edge
        {
            public int from;

            public int to;
            public long dist;
            
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }
        }
    }
    
    struct ModInt
    {
        public long value;
        private const int MOD = 1000000007;
        //private const int MOD = 998244353;

        public ModInt(long value) { this.value = value; }
        public static implicit operator ModInt(long a)
        {
            var ret = a % MOD;
            return new ModInt(ret < 0 ? (ret + MOD) : ret);
        }
        public static ModInt operator +(ModInt a, ModInt b) => (a.value + b.value);
        public static ModInt operator -(ModInt a, ModInt b) => (a.value - b.value);
        public static ModInt operator *(ModInt a, ModInt b) => (a.value * b.value);
        public static ModInt operator /(ModInt a, ModInt b) => a * Modpow(b, MOD - 2);
        public static ModInt operator <<(ModInt a, int n) => (a.value << n);
        public static ModInt operator >>(ModInt a, int n) => (a.value >> n);
        public static ModInt operator ++(ModInt a) => a.value + 1;
        public static ModInt operator --(ModInt a) => a.value - 1;
        public static ModInt Modpow(ModInt a, long n)
        {
            var k = a;
            ModInt ret = 1;
            while (n > 0)
            {
                if ((n & 1) != 0) ret *= k;
                k *= k;
                n >>= 1;
            }
            return ret;
        }
        private static readonly List<long> Factorials = new List<long>() { 1 };
        public static ModInt Fac(long n)
        {
            for (var i = Factorials.Count(); i <= n; i++)
            {
                Factorials.Add((Factorials[i - 1] * i) % MOD);
            }
            return Factorials[(int)n];
        }
        public static ModInt nCr(long n, long r)
        {
            return n < r ? 0 : Fac(n) / (Fac(r) * Fac(n - r));
        }
        public static explicit operator int(ModInt a) => (int)a.value;
    }
    static class IO_ShortCut
    {
        public static string[] _ReadSplit => Console.ReadLine().Split();
        public static int[] _ReadSplitInt => ConvertAll(Console.ReadLine().Split(), int.Parse);
        public static long[] _ReadSplitLong => ConvertAll(Console.ReadLine().Split(), long.Parse);
        public static double[] _ReadSplit_Double => ConvertAll(Console.ReadLine().Split(), double.Parse);
        public static string Str => Console.ReadLine();
        public static int Int => int.Parse(Console.ReadLine());
        public static long Long => long.Parse(Console.ReadLine());
        public static double Double => double.Parse(Console.ReadLine());
        public static T Conv<T>(string input)
        {
            if (typeof(T).Equals(typeof(ModInt)))
            {
                return (T)(dynamic)(long.Parse(input));
            }
            return (T)Convert.ChangeType(input, typeof(T));
        }
        public static void Input<T>(out T a) => a = Conv<T>(Console.ReadLine());
        public static void Input<T, U>(out T a, out U b)
        { var q = _ReadSplit;a = Conv<T>(q[0]);b = Conv<U>(q[1]); }
        public static void Input<T, U, V>(out T a, out U b, out V c)
        { var q = _ReadSplit;a = Conv<T>(q[0]);b = Conv<U>(q[1]);c = Conv<V>(q[2]); }
        public static void Input<T, U, V, W>(out T a, out U b, out V c, out W d)
        { var q = _ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]);d = Conv<W>(q[3]); }
        public static void Input<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
        { var q = _ReadSplit;a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]); d = Conv<W>(q[3]); e = Conv<X>(q[4]); }

        public static void OutL(object s) => Console.WriteLine(s);
        public static void Out_Sep<T>(IEnumerable<T> s) => Console.WriteLine(string.Join(" ", s));
        public static void Out_Sep<T>(IEnumerable<T> s, string sep) => Console.WriteLine(string.Join($"{sep}", s));
        public static void Out_Sep(params object[] s) => Console.WriteLine(string.Join(" ", s));
        public static void Out_One(object s) => Console.Write($"{s} ");
        public static void Out_One(object s, string sep) => Console.Write($"{s}{sep}");
        public static void Endl() => Console.WriteLine();
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            array = ConvertAll(array, x => initialvalue);
        }
        static public void Swap<T>(ref T a, ref T b)
        {
            T keep = a;
            a = b;
            b = keep;
        }
        static public void Display<T>(T[,] array2d, int n, int m)
        {
            for (var i = 0; i < n; i++)
            {
                for (var j = 0; j < m; j++)
                {
                    Console.Write($"{array2d[i, j]} ");
                }
                Console.WriteLine();
            }
        }
        static public long Gcd(long a,long b)
        {
            if (a == 0 || b == 0) return Max(a, b);
            return a % b == 0 ? b : Gcd(b, a % b);
        }
        static public long LPow(int a, int b) => (long)Pow(a, b);
        static public bool Bit(long x, int dig) => ((1L << dig) & x) != 0;
        static public int Sig(long a) => a == 0 ? 0 : (int)(a / Abs(a));
    }
}