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.*;
import java.util.*;
public class ClassA{
    public static void main(String args[])throws IOException{
       BufferedReader inp;
       inp=new BufferedReader(new InputStreamReader(System.in));
        String line[]=inp.readLine().split(" ");
        int n=Integer.parseInt(line[0]);
        int k=Integer.parseInt(line[1]);
        boolean b[]=new boolean[n*k+1];
        int a[]=new int[k];
        line=inp.readLine().split(" ");
        for(int i=0;i<k;i++){
            b[Integer.parseInt(line[i])]=true;
            a[i]=Integer.parseInt(line[i]);
        }
        int i=1;
        int j=0;
        while(j<k){
            int p=0;
            System.out.print(a[j]+" ");
            j++;
            for(;i<=k*n;i++){
                if(!b[i]){
                    System.out.print(i+" ");
                    p++;
                }
                if(p==n-1){
                    System.out.println("");i++;
                    break;
                }
            }
        }

    } 
}