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.NoSuchElementException;
import java.util.Objects;

public class DividingOrange {

    public static void main(String[] args) {
        Reader read = new Reader();

        int n = read.nextInt();
        int k = read.nextInt();
        int[][] values = new int[k+1][n+1];
        boolean[] out = new boolean[n*k+1];

        for(int i=1; i<= k; i++){
            values[i][1] = read.nextInt();
            out[values[i][1]] = true;
        }

        int v = 1;
        for(int i=1;i <values.length; i++) {
            for(int j=2; j<values[i].length; j++) {
                    while (v < out.length && out[v])
                        v++;
                    values[i][j] = v;
                    out[v] = true;
            }
        }

        for(int i=1; i<values.length; i++) {
            for(int j=1; j<values[i].length; j++) {
                System.out.print(values[i][j]+" ");
            }
            System.out.print("\n");
        }
    }

    private static class Reader {

        private final BufferedReader reader;
        private final String separator;
        private String ln;
        private String[] tokens;
        private int ptr;

        Reader(String separator, InputStream input) {
            this.reader = new BufferedReader(new InputStreamReader(input));
            this.separator = separator;
            this.ptr = -1;
        }

        Reader(String separator) { this(separator, System.in); }

        Reader() { this(" "); }

        String nextStr(){
            if (Objects.isNull(ln)) {
                try {
                    ln = reader.readLine();
                } catch (IOException e) {
                    System.out.println(e.getMessage());
                }
                if (Objects.nonNull(ln)) {
                    tokens = ln.split(separator);
                    ptr = 0;
                } else {
                    throw new NoSuchElementException("no next element");
                }

            } else if (ptr == tokens.length) {
                ln = null;
                tokens = null;
                ptr = -1;
                return nextStr();
            }

            return tokens[ptr++];
        }

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

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

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