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.io.BufferedReader;
import java.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Main {
	
	public static void main(String[] args) throws IOException {
		try(Scanner sc = new Scanner(System.in)){
			final int N = sc.nextInt();
			final int A = sc.nextInt();
			final int B = sc.nextInt();
			
			ArrayList<LinkedList<Integer>> units = new ArrayList<LinkedList<Integer>>();
			for(int i = 0; i < B; i++){ units.add(new LinkedList<Integer>()); }
			
			int rest = N;
			/*
			for(int i = A - 1; i >= 0; i--){
				units.get(0).addLast(N - i);
				rest--;
			}
			*/
			
			for(int i = 0; i < B; i++){
				final int curr_rest = rest;
				for(int j = 0; j < Math.min(A, curr_rest - (B - (i + 1))); j++){
					//System.out.println(rest);
					units.get(i).addFirst(rest);
					rest--;
				}
			}
			
			boolean flg = true;
			int curr_A = 0;
			for(final LinkedList<Integer> list : units){
				flg &= !list.isEmpty();
				curr_A = Math.max(curr_A, list.size());
			}
			//System.out.println(rest + " : " + units);
			
			if(rest != 0 || !flg || curr_A != A){
				System.out.println(-1);
			}else{
				boolean first = true;
				for(final LinkedList<Integer> list : units){
					for(final int id : list){
						System.out.print((first ? "" : " ") + id);
						first = false;
					}
				}
				System.out.println();
			}
			
			
			
		}
	}

	public static class Scanner implements Closeable {
		private BufferedReader br;
		private StringTokenizer tok;

		public Scanner(InputStream is) throws IOException {
			br = new BufferedReader(new InputStreamReader(is));
		}

		private void getLine() throws IOException {
			while (!hasNext()) {
				tok = new StringTokenizer(br.readLine());
			}
		}

		private boolean hasNext() {
			return tok != null && tok.hasMoreTokens();
		}

		public String next() throws IOException {
			getLine();
			return tok.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public int[] nextIntArray(int n) throws IOException {
			final int[] ret = new int[n];
			for (int i = 0; i < n; i++) {
				ret[i] = this.nextInt();
			}
			return ret;
		}

		public long[] nextLongArray(int n) throws IOException {
			final long[] ret = new long[n];
			for (int i = 0; i < n; i++) {
				ret[i] = this.nextLong();
			}
			return ret;
		}

		public void close() throws IOException {
			br.close();
		}
	}
}