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.util.ArrayList;
import java.util.Arrays;

public class Main {
    
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String nk = br.readLine();
        String k = br.readLine();
        String[] nkD = nk.split(" ");
        String[] kD = k.split(" ");
        int nxk = Integer.parseInt(nkD[0]) * Integer.parseInt(nkD[1]);
        ArrayList<Integer> numeros = new ArrayList<>();
        ArrayList<niño> niños = new ArrayList<>();
        
        for (int i = 0; i < nxk; i++) {
            numeros.add(i + 1);
        }
        
        for (int i = 0; i < Integer.parseInt(nkD[1]); i++) {
            int indexOf = numeros.indexOf(Integer.parseInt(kD[i]));
            numeros.remove(indexOf);
            niño nuevoN = new niño();
            nuevoN.trozos.add(Integer.parseInt(kD[i]));
            niños.add(nuevoN);
        }
        
        int index = 0;
        int c = 0;
        for (int i = 0; i < numeros.size(); i++) {
            if (c != Integer.parseInt(nkD[0]) - 1) {
                niños.get(index).trozos.add(numeros.get(i));
                c++;
            } else {
                c = 0;
                index++;
                i--;
            }
        }
        
        for (int i = 0; i < niños.size(); i++) {
            System.out.println(niños.get(i));
        }
    }
}

class niño {
    
    ArrayList<Integer> trozos = new ArrayList<>();
    
    @Override
    public String toString() {
        String toString = "";
        for (int i = 0; i < trozos.size(); i++) {
            if (i != trozos.size() - 1) {
                toString += trozos.get(i) + " ";
            } else {
                toString += trozos.get(i);
            }
        }
        return toString;
    }
}