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.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class ladders244a {
    static BufferedReader __in;
    static PrintWriter __out;
    static StringTokenizer input;

    public static void main(String[] args) throws IOException {
        __in = new BufferedReader(new InputStreamReader(System.in));
        __out = new PrintWriter(new OutputStreamWriter(System.out));

        read();
        int n = nextInt(), k = nextInt();
        boolean[] used = new boolean[n * k];
        int i = 0;
        int[][] ans = new int[k][n];
        read();
        for(int j = 0; j < k; ++j) {
            int x = nextInt();
            ans[j][0] = x;
            used[x - 1] = true;
        }
        for(int j = 0; j < k; ++j) {
            for(int l = 1; l < n; ++l) {
                while(used[i]) ++i;
                ans[j][l] = i + 1;
                used[i++] = true;
            }
        }
        for(int j = 0; j < k; ++j) {
            for(int l = 0; l < n - 1; ++l) {
                print(ans[j][l]);
                print(' ');
            }
            println(ans[j][n - 1]);
        }

        close();
    }

    static final int IMAX = 2147483647;
    static final long LMAX = 9223372036854775807L;
    static void read() throws IOException {input = new StringTokenizer(__in.readLine());}
    static String readLine() throws IOException {return __in.readLine();}
    static int nextInt() {return Integer.parseInt(input.nextToken());}
    static int readInt() throws IOException {return Integer.parseInt(__in.readLine());}
    static void print(Object o) {__out.print(o);}
    static void println(Object o) {__out.println(o);}
    static void println() {__out.println();}
    static void close() {__out.close();}
}