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

/**
 * This program finds the total number of polyndromes
 * from dictionary, as well as output total time that it took.
 *
 * @author Magzhan
 *
 * @version 1.0.0
 */
public class Main {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        try {

            Scanner in = new Scanner(System.in);

            int n=in.nextInt();
            int k=in.nextInt();

            int[] a = new int[k];
            Boolean[] b = new Boolean[n*k];

            for(int i=0;i<n*k;i++){
                b[i]=false;
            }

            for(int i=0;i<k;i++){
                a[i]=in.nextInt();
                b[a[i]-1]=true;
            }

            int c=0,p=0;

            for(int i=0;i<k;i++){
                System.out.print(a[i]+" ");
                p=0;
                while (p<n-1 && c<n*k) {
                    if(b[c]==false){
                        System.out.print((c+1) + " ");
                        p++;
                    }
                    c++;
                }
                System.out.println();
            }

            
        } catch(Exception e) {
            System.out.println(e.toString());
        }
    }

}