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.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.StringTokenizer;

public class Main implements Runnable {

	private int[] dp;
	private int n;
	private int k;
	private ArrayList<Integer> ar;
	private String[] s;

	private void solve() throws IOException {
		n = nextInt();
		k = nextInt();
		ar = new ArrayList<Integer>();
		for (int i = 0; i < k; i++) {
			ar.add(nextInt());
		}
		int c = 1;
		for (int x : ar) {
			out.print(x);
			for (int i = 2; i <= n;) {
				if (!ar.contains(c)) {
					out.print(" " + (c++));
					i++;
				} else {
					c++;
				}
			}
			out.println();
		}
	}

	private boolean check(int x) {
		for (int i = x; i <= k + x; i++) {
			int sum = 0;
			for (int j = 1; j <= n; j++) {
				sum += dp[(i - 1) * k + j];
			}
			if (sum != -1) {
				return false;
			}
		}
		return true;
	}

	private BufferedReader in;
	private PrintWriter out;
	private StringTokenizer st;

	String next() throws IOException {
		while (!st.hasMoreTokens()) {
			String line = in.readLine();
			if (line == null) {
				return null;
			}
			eat(line);
		}
		return st.nextToken();
	}

	int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	long nextLong() throws IOException {
		return Long.parseLong(next());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	private void eat(String s) {
		st = new StringTokenizer(s);
	}

	public static void main(String[] args) throws IOException {
		new Thread(null, new Main(), "Main", 1 << 27).start();
	}

	@Override
	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(new OutputStreamWriter(System.out));
			eat("");
			solve();
			in.close();
			out.close();
		} catch (IOException e) {
			e.printStackTrace();
			System.exit(567);
		}
	}

}