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.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

/**
 *
 * @author Artem_Mikhalevitch
 */
public class Solver extends ASolver {

    private int n;
    private int k;
    boolean[] reserved;
    int[] a;

    public static void main(String[] args) {
        Solver s = new Solver();
        s.init();
        if (s.readData()) {
            s.solve();
        }
    }

    @Override
    public void init() {
        super.init();

    }

    @Override
    public boolean readData() {
        try {
            n = nextInt();
            k = nextInt();
            reserved = new boolean[n * k + 1];
            a = new int[k];
            for (int i = 0; i < k; i++) {
                a[i] = nextInt();
                reserved[a[i]] = true;
            }
        } catch (IOException ex) {
            System.out.println(ex.getCause());
            System.out.println(ex.getMessage());
            return false;
        }
        return true;
    }

    public void solve() {
        int lastReserved = 1;
        for (int i = 0; i < k; i++) {
            lastReserved = printK(lastReserved, a[i]);
        }
    }

    public int printK(int lastReserved, int currentValue) {
        int i = lastReserved;
        StringBuilder sb = new StringBuilder(2 * n);
        boolean isPrinted = false;
        int j = 0;
        if (currentValue <= lastReserved) {
            sb.append(currentValue).append(" ");
            isPrinted = true;
            j++;
        }
        while (i <= n * k && j < n) {
            if (j == n - 1 && currentValue > i) {
                sb.append(currentValue).append(" ");
                break;
            }
            if ((!isPrinted && currentValue == i)) {
                sb.append(currentValue).append(" ");
                isPrinted = true;
                j++;
                i++;
            } else if (!reserved[i]) {
                sb.append(i).append(" ");
                j++;
                i++;
            } else {
                i++;
            }
        }
        this.writeData(sb.toString());
        return i;
    }
}

abstract class ASolver {

    protected StringTokenizer tokens;
    protected BufferedReader input;
    protected PrintWriter output;

    public void init() {
        input = new BufferedReader(new InputStreamReader(System.in));
    }

    public abstract boolean readData();

    public void writeData(String result) {
        System.out.println(result);
    }

    public void writeData(int result) {
        System.out.println(result);
    }

    public void writeData(long result) {
        System.out.println(result);
    }

    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());
    }

    public String next() throws IOException {
        while (tokens == null || !tokens.hasMoreTokens()) {
            tokens = new StringTokenizer(input.readLine());
        }
        return tokens.nextToken();
    }

    public long infinityImitator(long a, long b) {
        if (a == Long.MIN_VALUE) {
            return Long.MIN_VALUE;
        } else {
            return a + b;
        }
    }

    public int infinityImitator(int a, int b) {
        if (a == Integer.MIN_VALUE) {
            return Integer.MIN_VALUE;
        } else {
            return a + b;
        }
    }

    public long max(long... a) {
        long result = Long.MIN_VALUE;
        for (int i = 0; i < a.length; i++) {
            result = Math.max(result, a[i]);
        }
        return result;
    }

    public int max(int... a) {
        int result = Integer.MIN_VALUE;
        for (int i = 0; i < a.length; i++) {
            result = Math.max(result, a[i]);
        }
        return result;
    }
}