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.Arrays;
import java.util.Scanner;
public class Problem {

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int n , k ;
        n = input.nextInt();
        k = input.nextInt();
        int [] segment = new int[k];
        int [] nk = new int[n*k+1];
        for ( int i = 0 ; i < k ; i++ ){
            segment[i] = input.nextInt();
            nk[segment[i]] = -1;
        }
        int counter = 1 ;
        int [][] res = new int [n][k];
        res[0] = Arrays.copyOf(segment,k);
        for ( int i = 1 ; i < n ; i++ ){
            for ( int j = 0 ; j < k ; j++ ){
                while ( nk[counter] == -1 )
                    counter++;
                res[i][j] = counter;
                counter++;
            }
        }
        for ( int i = 0 ; i < k; i++ ){
            for ( int j = 0 ; j< n ; j++ )
                System.out.print(res[j][i]+" ");
            System.out.println();
        }  
    }
}