Problem: Recently Pashmak has been employed in a transportation company. The company has k buses and has a contract with a school which has n students. The school planned to take the students to d different places for d days (each day in one place). Each day the company provides all the buses for the trip. Pashmak has to arrange the students in the buses. He wants to arrange the students in a way that no two students become close friends. In his ridiculous idea, two students will become close friends if and only if they are in the same buses for all d days.

Please help Pashmak with his weird idea. Assume that each bus has an unlimited capacity.

Input

The first line of input contains three space-separated integers n, k, d (1 ≤ n, d ≤ 1000; 1 ≤ k ≤ 109).

Output

If there is no valid arrangement just print -1. Otherwise print d lines, in each of them print n integers. The j-th integer of the i-th line shows which bus the j-th student has to take on the i-th day. You can assume that the buses are numbered from 1 to k.

Examples

Input

3 2 2


Output

1 1 2 
1 2 1 


Input

3 2 1


Output

-1

Note

Note that two students become close friends only if they share a bus each day. But the bus they share can differ from day to day.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringTokenizer;

public class Solution {

	static InputReader in = new InputReader(System.in);
	static int mod = (int) (1e9 + 7);
	static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(
			System.out));

	private static int divCeil(int x, int y) {
		int res = x / y;
		if (x % y > 0) {
			++res;
		}
		return res;
	}

	public static void main(String[] args) throws IOException {

		int n = in.nextInt();
		int k = in.nextInt();
		int d = in.nextInt();

		StringBuilder[] res = new StringBuilder[d];

		for (int i = 0; i < res.length; i++) {
			res[i] = new StringBuilder();
		}

		int[] arr = new int[d];
		Arrays.fill(arr, 1);

		if (divCeil(n, (int) Math.pow(k, d)) > 1) {
			out.write("-1");
		} else {

			int count = 1;

			for (int j = 0; j < d; j++) {
				res[j].append(" ").append(arr[j]);
			}

			while (count < n) {

				arr[d - 1]++;

				if (arr[d - 1] > k) {

					arr[d - 1] = 1;

					for (int i = d - 2; i >= 0; i--) {
						if (arr[i] + 1 > k) {
							arr[i] = 1;
						} else {
							arr[i]++;
							break;
						}
					}

				}

				for (int j = 0; j < d; j++) {
					res[j].append(" ").append(arr[j]);
				}

				count++;
			}

			for (int i = res.length - 1; i >= 0; i--) {
				out.write(res[i].toString().trim());
				out.newLine();
			}
		}

		out.flush();
	}
}

class ListComparator implements Comparator<Integer> {

	@Override
	public int compare(Integer e1, Integer e2) {
		return e2.compareTo(e1);
	}
}

class ArrayComparator implements Comparator<int[]> {
	@Override
	public int compare(int[] o1, int[] o2) {

		long res1 = Math.abs(o1[0]) + Math.abs(o1[1]);
		long res2 = Math.abs(o2[0]) + Math.abs(o2[1]);
		return Long.compare(res1, res2);
	}
};

class Pair {

	int x;
	int y;

	public Pair(int x, int y) {
		this.x = x;
		this.y = y;
	}

	@Override
	public String toString() {
		return "Pair [x=" + x + ", y=" + y + "]";
	}
}

class InputReader {
	private BufferedReader reader;
	private StringTokenizer tokenizer;

	public InputReader(InputStream stream) {
		reader = new BufferedReader(new InputStreamReader(stream), 32768);
		tokenizer = null;
	}

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

	public String readLine() {
		try {
			return reader.readLine();
		} catch (IOException e) {
			throw new RuntimeException(e);
		}
	}

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

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

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

	public float nextFloat() {
		return Float.parseFloat(next());
	}

}