Problem: One day Ms Swan bought an orange in a shop. The orange consisted of n·k segments, numbered with integers from 1 to n·k. 

There were k children waiting for Ms Swan at home. The children have recently learned about the orange and they decided to divide it between them. For that each child took a piece of paper and wrote the number of the segment that he would like to get: the i-th (1 ≤ i ≤ k) child wrote the number ai (1 ≤ ai ≤ n·k). All numbers ai accidentally turned out to be different.

Now the children wonder, how to divide the orange so as to meet these conditions:

  * each child gets exactly n orange segments; 
  * the i-th child gets the segment with number ai for sure; 
  * no segment goes to two children simultaneously. 



Help the children, divide the orange and fulfill the requirements, described above.

Input

The first line contains two integers n, k (1 ≤ n, k ≤ 30). The second line contains k space-separated integers a1, a2, ..., ak (1 ≤ ai ≤ n·k), where ai is the number of the orange segment that the i-th child would like to get.

It is guaranteed that all numbers ai are distinct.

Output

Print exactly n·k distinct integers. The first n integers represent the indexes of the segments the first child will get, the second n integers represent the indexes of the segments the second child will get, and so on. Separate the printed numbers with whitespaces.

You can print a child's segment indexes in any order. It is guaranteed that the answer always exists. If there are multiple correct answers, print any of them.

Examples

Input

2 2
4 1


Output

2 4 
1 3 


Input

3 1
2


Output

3 2 1 

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        int n = Reader.nextInt();
        int k = Reader.nextInt();

        int[] a = new int[k];
        Set<Integer> notFree = new HashSet<>();
        for (int i = 0; i < a.length; i++){
            a[i] = Reader.nextInt();
            notFree.add(a[i]);
        }

        int counter = 1;
        for (int i = 0; i < k; i++) {
            StringBuilder ansForKid = new StringBuilder();
            ansForKid.append(a[i]);
            for (int j = 1; j < n; j++) {
                if (notFree.contains(counter)){
                    counter++;
                    j--;
                }
                else {
                    ansForKid.append(" ").append(counter);
                    notFree.add(counter);
                }
            }

            System.out.println(ansForKid);
        }


    }
}

class Reader{
    private static BufferedReader reader;
    private static StringTokenizer tokenizer;
    static void init(InputStream inputStream){
        reader = new BufferedReader(new InputStreamReader(inputStream));
        tokenizer = new StringTokenizer("");
    }
    static String next() throws IOException {
        String read;
        while (!tokenizer.hasMoreTokens()){
            read = reader.readLine();
            if (read == null || read.equals(""))
                return "-1";
            tokenizer = new StringTokenizer(read);
        }

        return tokenizer.nextToken();
    }
    static int nextInt() throws IOException{
        return Integer.parseInt(next());
    }

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

    //Get a whole line.
//    static String line() throws IOException{
//        return reader.readLine();
//    }
//
//    static double nextDouble() throws IOException{return Double.parseDouble(next());}
}