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.*;

public class Main {
	public static void main(String[] args){
		Scanner s = new Scanner(System.in);
		final int n = s.nextInt();
		final int k = s.nextInt();
		int [] chosen = new int[k];
		boolean [] used = new boolean[n*k + 1];
		for (int i = 0; i < k; ++i){
			final int a = s.nextInt();
			chosen[i] = a;
			used[a] = true;
		}
		for (int i = 0, c = 1; i < k; ++i){
			System.out.print(chosen[i] + " ");
			for (int j = 0; j < n - 1; ++c){
				if (!used[c]){
					used[c] = true;
					j++;
					System.out.print(c + " ");
				}
			}
		}
		System.out.println();
	}
}