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)

// author: camypaper
using System;
using System.Linq;
using System.Collections.Generic;
using System.Diagnostics;
using Debug = System.Diagnostics.Trace;
using SB = System.Text.StringBuilder;
using static System.Math;
using static System.Numerics.BigInteger;
using static Program.IO.Scanner;
using Number = System.Int64;

#region IO
namespace Program.IO {
	using System.IO;
	using System.Text;
	using System.Globalization;

	public class Printer : StreamWriter {
		public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
		public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
	}
	static public class Scanner {
		public static StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
		public static int ri => sc.Integer();
		public static long rl => sc.Long();
		public static string rs => sc.Scan();
		public static double rd => sc.Double();
	}
	public class StreamScanner {
		public StreamScanner(Stream stream) { str = stream; }

		public readonly Stream str;
		private readonly byte[] buf = new byte[1024];
		private int len, ptr;
		public bool isEof = false;
		public bool IsEndOfStream { get { return isEof; } }

		private byte read() {
			if (isEof) return 0;
			if (ptr >= len) {
				ptr = 0;
				if ((len = str.Read(buf, 0, 1024)) <= 0) {
					isEof = true;
					return 0;
				}
			}
			return buf[ptr++];
		}

		public char Char() {
			byte b = 0;
			do b = read(); while ((b < 33 || 126 < b) && !isEof);
			return (char)b;
		}
		public string Scan() {
			var sb = new StringBuilder();
			for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
			return sb.ToString();
		}
		public string ScanLine() {
			var sb = new StringBuilder();
			for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
			return sb.ToString();
		}
		public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
		public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
		public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
	}

}

#endregion

#region main
static class Ex {
	static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
	static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
		return string.Join(st, ie);
	}
	static public void Main() {
		Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = true });
		var solver = new Program.Solver();
		var t = new System.Threading.Thread(solver.Solve, 100000000);
		t.Start();
		t.Join();
		//*/
		//solver.Solve();
		Console.Out.Flush();
	}
}
#endregion

namespace Program {
	public class Solver {
		Random rnd = new Random(0);
		public void Solve() {
			var n = ri;
			var k = ri;
			if (2 * k > n + 1) {
				Console.WriteLine(-1);
				return;
			}
			var ans = Enumerate(n, x => new int[3]);
			for (int i = 0; i < n; i++) ans[i][2] = 2 * n + i;

			var X = (n + 1) / 2;
			var Y = n - X;
			for (int i = 0; i < X; i++) {
				ans[i * 2][0] += i;
				ans[i * 2][1] += n - 1 - (X - 1) + i;
			}
			for (int i = 0; i < Y; i++) {
				ans[i * 2 + 1][0] += i + X;
				ans[i * 2 + 1][1] += n - 1 - X - (Y - 1) + i;
			}


			for (int i = 0; i < n; i++) {
				ans[i][1] += n;
				for (int j = 0; j < 3; j++) ans[i][j] += k;
			}
			foreach (var x in ans)
				Console.WriteLine(x.AsJoinedString());
		}

		const long INF = 1L << 60;
		static int[] dx = { -1, 0, 1, 0 };
		static int[] dy = { 0, 1, 0, -1 };
		static T[] Enumerate<T>(int n, Func<int, T> f) {
			var a = new T[n]; for (int i = 0; i < a.Length; ++i) a[i] = f(i); return a;
		}
		static T[][] Enumerate<T>(int n, int m, Func<int, int, T> f) {
			return Enumerate(n, x => Enumerate(m, y => f(x, y)));
		}
		static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
	}
}

#region ModInt
/// <summary>
/// [0,<see cref="Mod"/>) までの値を取るような数
/// </summary>
public struct ModInt {
	public const long Mod = 998244353;
	public long num;
	public ModInt(long n) { num = n; }
	public override string ToString() { return num.ToString(); }
	public static ModInt operator +(ModInt l, ModInt r) { return new ModInt(l.num + r.num < Mod ? l.num + r.num : l.num + r.num - Mod); }
	public static ModInt operator -(ModInt l, ModInt r) { return new ModInt(l.num + Mod - r.num < Mod ? l.num + Mod - r.num : l.num - r.num); }
	public static ModInt operator *(ModInt l, ModInt r) { return new ModInt(l.num * r.num % Mod); }
	public static ModInt operator /(ModInt l, ModInt r) { return l * Inverse(r); }
	public static implicit operator ModInt(long n) { return new ModInt(n); }
	public static ModInt Pow(ModInt v, long k) { return Pow(v.num, k); }
	public static ModInt Pow(long v, long k) {
		long ret = 1;
		for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
			if ((k & 1) == 1) ret = ret * v % Mod;
		return new ModInt(ret);
	}
	public static ModInt Inverse(ModInt v) { return Pow(v, Mod - 2); }
	public static ModInt Modulo(long v) { return new ModInt(((v % Mod) + Mod) % Mod); }
}
#endregion

#region Binomial Coefficient
public class BinomialCoefficient {
	public ModInt[] fact, ifact;
	public BinomialCoefficient(int n) {
		fact = new ModInt[n + 1];
		ifact = new ModInt[n + 1];
		fact[0] = 1;
		for (int i = 1; i <= n; i++)
			fact[i] = fact[i - 1] * i;
		ifact[n] = ModInt.Inverse(fact[n]);
		for (int i = n - 1; i >= 0; i--)
			ifact[i] = ifact[i + 1] * (i + 1);
		ifact[0] = ifact[1];
	}
	public ModInt this[int n, int r] {
		get {
			if (n < 0 || n >= fact.Length || r < 0 || r > n) return 0;
			return fact[n] * ifact[n - r] * ifact[r];
		}
	}
	public ModInt RepeatedCombination(int n, int k) {
		if (k == 0) return 1;
		return this[n + k - 1, k];
	}
}
#endregion
#region ModFFT
static class ModFFT {
	public const int MOD = 998244353;
	static readonly int[] roots;
	static ModFFT() {
		for (int i = 2; i * i <= MOD; i++) if (MOD % i == 0) throw new Exception();
		int t, p2;
		for (t = MOD - 1, p2 = 0; t % 2 == 0; t /= 2, p2++) ;
		if (p2 == 0) throw new Exception();
		roots = new int[p2 + 1];
		int s;
		for (s = 2; ; s++) if (ModPow(s, (MOD - 1) / 2) != 1) break;
		var pw = MOD - 1;
		for (int i = 0; i < p2; i++, pw /= 2)
			roots[i] = ModPow(s, pw);
	}
	static public int ModPow(long a, int k) {
		long ret = 1;
		for (; k > 0; a = (a * a) % MOD, k /= 2)
			if (k % 2 == 1) ret = (ret * a) % MOD;
		return (int)ret;
	}
	static void fft(int[] a, bool inv) {
		var n = a.Length;
		for (int i = 0, j = 1; j < n - 1; ++j) {
			for (int k = n >> 1; k > (i ^= k); k >>= 1) ;
			if (j < i) { var tmp = a[i]; a[i] = a[j]; a[j] = tmp; }
		}
		for (int p2 = 1, pow2 = 1; p2 < n; p2 *= 2, pow2++) {
			var w = roots[pow2];
			if (inv) w = ModPow(w, MOD - 2);
			for (int big = 0; big < n; big += 2 * p2) {
				int cur = 1;
				for (int small = big; small < big + p2; ++small) {
					int i = small;
					int j = small + p2;
					int u = a[i];
					int o = a[j];
					int v = (int)(o * (long)cur % MOD);
					a[i] = u + v;
					if (a[i] >= MOD) a[i] -= MOD;
					a[j] = u - v;
					if (a[j] < 0) a[j] += MOD;
					cur = (int)(cur * (long)w % MOD);
				}
			}

		}
	}
	static public int[] Convolute(int[] a, int[] b) {
		var k = 1;
		while (k < a.Length + b.Length - 1) k *= 2;
		var aa = new int[k]; Array.Copy(a, aa, a.Length);
		var bb = new int[k]; Array.Copy(b, bb, b.Length);
		fft(aa, false);
		fft(bb, false);
		var c = new int[k];
		for (int i = 0; i < k; i++)
			c[i] = (int)(Math.BigMul(aa[i], bb[i]) % MOD);
		fft(c, true);
		var inv = ModPow(k, MOD - 2);
		for (int i = 0; i < k; i++)
			c[i] = (int)(Math.BigMul(c[i], inv) % MOD);
		return c;
	}
}
#endregion