Problem: Determine if there exists a sequence obtained by permuting 1,2,...,N that satisfies the following conditions:

* The length of its longest increasing subsequence is A.
* The length of its longest decreasing subsequence is B.



If it exists, construct one such sequence.

Constraints

* 1 \leq N,A,B \leq 3\times 10^5
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N A B


Output

If there are no sequences that satisfy the conditions, print `-1`.

Otherwise, print N integers. The i-th integer should be the i-th element of the sequence that you constructed.

Examples

Input

5 3 2


Output

2 4 1 5 3


Input

7 7 1


Output

1 2 3 4 5 6 7


Input

300000 300000 300000


Output

-1

Solution (in JAVA):

Solution:

import java.util.Arrays;

public class Main {


  private static void solve() {
    int n = ni();
    long a = ni();
    long b = ni();
    
    if ((long)a * b < n || a + b > n + 1) {
      System.out.println(-1);
      return;
    }
    
    long[][] arr = new long[n][3];
    int ptr = 0;
    for (int i = 0; i < b; i ++) {
      arr[ptr][0] = b - i;
      arr[ptr][1] = i;
      ptr ++;
    }
    
    for (int i = 0; i < a - 1; i ++) {
      arr[ptr][0] = b * (i + 2);
      arr[ptr][1] = (i + 1) * b;
      ptr ++;
    }
    
    long pos = b + 1;
    long val = b * 2 - 1;
    while (ptr < n) {
      for (int i = 0; ptr < n && i < b - 1; i ++) {
        arr[ptr][0] = val --;
        arr[ptr][1] = pos ++;
        ptr ++;
      }
      pos ++;
      val += 2 * b - 1;
    }
    Arrays.sort(arr, (o1, o2) -> Long.signum(o1[0] - o2[0]));
    for (int i = 0; i < n; i ++) {
      arr[i][2] = i + 1;
    }
    Arrays.sort(arr, (o1, o2) -> Long.signum(o1[1] - o2[1]));
    StringBuilder sb = new StringBuilder();
    for (int i = 0; i < n; i ++) {
      sb.append(arr[i][2]);
      if (i < n - 1) sb.append(" ");
    }
    System.out.println(sb);
  }

  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));
  }
}