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.math.BigInteger;
import java.util.*;
import java.io.*;

import static java.lang.Math.*;

public class Main {
    FastIO io;

    int n, d, k;

    // File names!!!

    void solve() throws Exception {
        n = io.nextInt();
        k = io.nextInt();
        d = io.nextInt();
        if (BigInteger.valueOf(k).pow(d).compareTo(BigInteger.valueOf(n)) < 0) {
            io.println(-1);
            return;
        }
        int[][] ans = new int[n][];
        int[] t = new int[d];
        for (int i = 0; i < n; i++) {
            ans[i] = Arrays.copyOf(t, t.length);
            t[d - 1]++;
            for (int j = d - 1; j > 0; j--) {
                t[j - 1] += t[j] / k;
                t[j] %= k;
            }
        }
        for (int i = 0; i < d; i++) {
            for (int j = 0; j < n; j++) {
                io.print(ans[j][i] + 1);
                io.print(" ");
            }
            io.println();
        }
    }

    void run() {
        try {
            io = new FastIO();
            solve();
            io.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(abs(-1));
        }
    }

    public static void main(String[] args) {
        try {
            Locale.setDefault(Locale.US);
        } catch (Exception ignore) {
        }
        new Main().run();
    }

    class FastIO extends PrintWriter {
        private BufferedReader in;
        private StringTokenizer stok;

        FastIO() {
            super(System.out);
            in = new BufferedReader(new InputStreamReader(System.in));
        }

        FastIO(String s) throws FileNotFoundException {
            super("".equals(s) ? "output.txt" : s + ".out");
            in = new BufferedReader(new FileReader("".equals(s) ? "input.txt" : s + ".in"));
        }

        @Override
        public void close() {
            super.close();
            try {
                in.close();
            } catch (IOException ignored) {
            }
        }

        String next() {
            while (stok == null || !stok.hasMoreTokens()) {
                try {
                    stok = new StringTokenizer(in.readLine());
                } catch (Exception e) {
                    return null;
                }
            }
            return stok.nextToken();
        }

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

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

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

        char nextChar() {
            try {
                return (char) in.read();
            } catch (IOException e) {
                return (char) -1;
            }
        }

        String nextLine() {
            try {
                return in.readLine();
            } catch (IOException e) {
                return null;
            }
        }

        char[] nextCharArray() {
            return next().toCharArray();
        }
    }

    void shuffleSort(int[] a) {
        Random rand = new Random();
        for (int i = 1; i < a.length; i++) {
            int x = rand.nextInt(i + 1);
            int chg = a[i];
            a[i] = a[x];
            a[x] = chg;
        }
        Arrays.sort(a);
    }

    class IntArray {
        private int capacity;
        private int[] data;
        private int size = 0;

        IntArray(int capacity) {
            this.capacity = capacity;
            this.data = new int[capacity];
        }

        IntArray() {
            this(16);
        }

        int get(int index) {
            return data[index];
        }

        void add(int x) {
            if (size == capacity) {
                int[] newData = new int[capacity * 2];
                System.arraycopy(data, 0, newData, 0, capacity);
                data = newData;
                capacity *= 2;
            }
            data[size++] = x;
        }
    }
}