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.DataInputStream;
import java.io.IOException;
import java.io.PrintWriter;

public class P459C5 {
    public static void main(String[] args) throws IOException {
        InputReader2 ir = new InputReader2();
        PrintWriter pw = new PrintWriter(System.out);

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

        if (k >= n) {
            StringBuilder sb = new StringBuilder(n * n);
            for (int i = 1; i <= n; i++) {
                sb.append(i).append(" ");
            }
            for (int i = 0; i < d; i++) {
                pw.println(sb);
            }
        } else if (k == 1) {
            pw.println(-1);
        } else if (pos(n, k, d)) {
            int[] num = new int[n];
            for (int i = 0; i < n; i++) {
                num[i] = i;
            }
            for (int i = 1; i <= d; i++) {
                for (int j = 0; j < n; j++) {
                    pw.print((num[j] % k) + 1 + " ");
                    num[j] /= k;
                }
                pw.println();
            }
        } else {
            pw.println(-1);
        }

        pw.close();
    }

    private static boolean pos(int n, int k, int d) {
        long res = 1;
        for (int i = 0; i < d; i++) {
            res *= k;
            if (res >= n) {
                return true;
            }
        }
        return false;
    }

    private static class InputReader2 {
        final private int BUFFER_SIZE = 1 << 16;
        private final DataInputStream dis;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;

        public InputReader2() {
            dis = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        private int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = dis.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
    }
}