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 A {
    public static void solution(BufferedReader reader, PrintWriter out)
            throws IOException {
        In in = new In(reader);
        int n = in.nextInt(), k = in.nextInt();
        boolean[] seg = new boolean[n * k + 1];
        int[] a = new int[k];
        for (int i = 0; i < k; i++) {
            a[i] = in.nextInt();
            seg[a[i]] = true;
        }
        for (int i = 0, j = 1; i < k; i++, j = 1) {
            seg[a[i]] = false;
            for (int cnt = 1; cnt <= n; cnt++) {
                while (seg[j])
                    j++;
                int cur = cnt == n && j < a[i] ? a[i] : j;
                seg[cur] = true;
                out.printf("%d ", cur);
            }
            out.println();
        }
    }

    public static void main(String[] args) throws Exception {
        BufferedReader reader = new BufferedReader(new InputStreamReader(
                System.in));
        PrintWriter out = new PrintWriter(new BufferedWriter(
                new OutputStreamWriter(System.out)));
        solution(reader, out);
        out.close();
    }

    protected static class In {
        private BufferedReader reader;
        private StringTokenizer tokenizer = new StringTokenizer("");

        public In(BufferedReader reader) {
            this.reader = reader;
        }

        public String next() throws IOException {
            while (!tokenizer.hasMoreTokens())
                tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }

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

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

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