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 Oranges {
	BufferedReader br;
	PrintWriter out;
	StringTokenizer stok;

	void solve() throws IOException {
			int n = nextInt();
			int k = nextInt();
			int[] a = new int[k];
			boolean[] b = new boolean[n*k];
			for (int i = 0; i < n*k; i++) {
				b[i] = true;
			}
			for (int i = 0; i < k; i++) {
				a[i] = nextInt()-1;
				b[a[i]] = false;
			}
			for (int i = 0; i < k; i++) {
				int c = 0;
				int i1 = 0;
				out.print(a[i]+1);
				out.print(" ");
				while (c < n-1) {
					if (b[i1]) {
						b[i1] = false;
						out.print(i1+1);
						out.print(" ");
						c++;
					}
					i1++;
				}
				out.println();
			}
	}

	String nextToken() throws IOException {
		while (stok == null || !stok.hasMoreTokens()) {
			String s = br.readLine();
			if (s == null) {
				return null;
			}
			stok = new StringTokenizer(s);
		}
		return stok.nextToken();
	}

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

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

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

	char nextChar() throws IOException {
		return (char) (br.read());
	}

	String nextLine() throws IOException {
		return br.readLine();
	}

	void run() throws IOException {
		// br = new BufferedReader(new FileReader("rmq.in"));
		// out = new PrintWriter("rmq.out");
		// br = new BufferedReader(new FileReader("input.txt"));
		// out = new PrintWriter("output.txt");
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		solve();
		br.close();
		out.close();
	}

	public static void main(String[] args) throws IOException {
		// Locale.setDefault(Locale.US);
		new Oranges().run();
	}
}