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.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;
import java.util.LinkedList;

public class E {
	public static void main(String[] args) {
		FastScannerE sc = new FastScannerE(System.in);
		
		int N = sc.nextInt();
		int K = sc.nextInt();
		int D = sc.nextInt();
		
		//check for -1
		int kids = N;
		for(int i = 0; i<D; i++){
			int ceil = kids / K;
			if(kids % K > 0) ceil++;
			kids = ceil;
		}
		
		if(kids > 1){
			System.out.println(-1);
		}
		else{
			StringBuilder sb = new StringBuilder();
			int[] list = new int[N];
			for(int i = 0; i<N; i++) list[i] = i;
			for(int d = 0; d<D; d++){
				
				int[] newlist = new int[N];
				int[] busses = new int[N];
				int ii = 0;
				for(int i = 0, min1 = Math.min(K, N); i < min1; i++){
					for(int j = i; j<N; j += K){
						int ind = list[j];
						newlist[ii] = ind;
						ii++;
						busses[ind] = i;
					}
				}
				list = newlist;
				
				for(int i : busses){
					sb.append(i + 1);
					sb.append(' ');
				}
				sb.setLength(sb.length() - 1);
				sb.append('\n');
			}
			System.out.print(sb);
		}
	}
}

class FastScannerE {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public FastScannerE(InputStream is) {
        stream = is;
    }

    public int read() {
        if (numChars == -1) throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try{
                numChars = stream.read(buf);
            }
            catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0) return -1;
        }
        return buf[curChar++];
    }

    public int nextInt(){
        int c = read();
        while (isSpaceChar(c)) c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9') throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public String next() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }  

    public double nextDouble() {
        int c = read();
        while (isSpaceChar(c)) c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E') return res * Math.pow(10, nextInt());
            if (c < '0' || c > '9') throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E') return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9') throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }
    
    public long nextLong() {
        int c = read();
        while (isSpaceChar(c)) c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9') throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
    
    public boolean isSpaceChar(int c) {
        if (filter != null) return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}