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:
// package com.MahmoudHamdy;

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

public class Main {

    static final int INF = (int) 2e9;
    static int n, k, d;
    static ArrayList<ArrayList<Integer>> arr;
    static ArrayList<Integer> temp;

    public static void main(String[] args) throws IOException {
//        Scanner Sc = new Scanner("input.txt");
//        PrintWriter Out = new PrintWriter(new FileWriter("output.txt"));
        Scanner Sc = new Scanner(System.in);
        PrintWriter Out = new PrintWriter(System.out);

        arr = new ArrayList<>();
        temp = new ArrayList<>();
        n = Sc.nextInt();
        k = Sc.nextInt();
        d = Sc.nextInt();
        solve();
        if(arr.size() < n)
            Out.print(-1);
        else
        {
            for(int i = 0; i < d; i++)
            {
                for(int j = 0; j < n; j++)
                    Out.print(arr.get(j).get(i) + " ");
                Out.println();
            }
        }

        Out.flush();
        Out.close();
    }

    static void solve()
    {
        if(temp.size() == d)
        {
            arr.add(new ArrayList<>(temp));
            return;
        }
        for(int i = 1; i<= k; i++)
        {
            temp.add(i);
            solve();
            temp.remove(temp.size() - 1);
            if(arr.size() >= n)
                return;
        }
    }


    static class Comp
    {
        TreeMap<Integer, Integer> mop = new TreeMap<>();
        TreeSet<Integer> st = new TreeSet<>();

        void add(int x)
        {
            st.add(x);
        }
        int get(int x)
        {
            return mop.get(x);
        }
        void compress()
        {
            for(int i : st)
                mop.put(i, mop.size());
        }
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }
        Scanner(String s) throws FileNotFoundException { br = new BufferedReader(new FileReader(s)); }


        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

    }

    static class pair implements Comparable<pair>{
        char f;long s;
        pair(char a,long b){f= a;s=b;}

        @Override
        public int compareTo(pair p) {
            if(s != p.s)
                return s > p.s ? 1 : -1;
            return f-p.f;
        }
    }
}