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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


public class Main {
  private static void solve() {
    int n = ni();
    long k = nl();


    long[][] a = new long[n][3];

    if (f(a, n, k, new int[] {0, 1})) {
      digit(a);
    } else {
      System.out.println(-1);
    }
  }

  private static void digit(long[][] a) {
    for (long[] v : a) {
      out.println(v[0] + " " + v[1] + " " + v[2]);
    }
  }

  private static boolean f(long[][] a, int n, long k, int[] offset) {
    int ptr = 0;
    for (long v = k + n, u = k + n / 2; v < k + n * 2; v += 2, u--) {
      a[ptr][0] = u;
      a[ptr][1] = v;
      ptr++;
    }

    for (long v = k + n + 1, u = k + n - 1; v < k + n * 2; v += 2, u--) {
      a[ptr][0] = u;
      a[ptr][1] = v;
      ptr++;
    }

    ptr = 0;
    for (long v = k + n * 2; v < k + n * 3; v++) {
      a[ptr][2] = v;
      if (a[ptr][0] + a[ptr][1] > a[ptr][2]) {
        return false;
      }
      ptr++;
    }
    return true;
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}