Problem: Phoenix loves beautiful arrays. An array is beautiful if all its subarrays of length k have the same sum. A subarray of an array is any sequence of consecutive elements.

Phoenix currently has an array a of length n. He wants to insert some number of integers, possibly zero, into his array such that it becomes beautiful. The inserted integers must be between 1 and n inclusive. Integers may be inserted anywhere (even before the first or after the last element), and he is not trying to minimize the number of inserted integers.

Input

The input consists of multiple test cases. The first line contains an integer t (1 ≤ t ≤ 50) — the number of test cases.

The first line of each test case contains two integers n and k (1 ≤ k ≤ n ≤ 100).

The second line of each test case contains n space-separated integers (1 ≤ a_i ≤ n) — the array that Phoenix currently has. This array may or may not be already beautiful.

Output

For each test case, if it is impossible to create a beautiful array, print -1. Otherwise, print two lines.

The first line should contain the length of the beautiful array m (n ≤ m ≤ 10^4). You don't need to minimize m.

The second line should contain m space-separated integers (1 ≤ b_i ≤ n) — a beautiful array that Phoenix can obtain after inserting some, possibly zero, integers into his array a. You may print integers that weren't originally in array a.

If there are multiple solutions, print any. It's guaranteed that if we can make array a beautiful, we can always make it with resulting length no more than 10^4.

Example

Input


4
4 2
1 2 2 1
4 3
1 2 2 1
3 2
1 2 3
4 4
4 3 4 2


Output


5
1 2 1 2 1
4
1 2 2 1
-1
7
4 3 2 1 4 3 2

Note

In the first test case, we can make array a beautiful by inserting the integer 1 at index 3 (in between the two existing 2s). Now, all subarrays of length k=2 have the same sum 3. There exists many other possible solutions, for example: 

  * 2, 1, 2, 1, 2, 1 
  * 1, 2, 1, 2, 1, 2 



In the second test case, the array is already beautiful: all subarrays of length k=3 have the same sum 5.

In the third test case, it can be shown that we cannot insert numbers to make array a beautiful.

In the fourth test case, the array b shown is beautiful and all subarrays of length k=4 have the same sum 10. There exist other solutions also.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class b{


    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        
        int t = sc.nextInt();
        for(int i=0; i<t; i++) {
            int n = sc.nextInt();
            int k = sc.nextInt();
            int[] arr = new int[n];
            for(int j=0; j<n; j++) {
                arr[j] = sc.nextInt();
            }
            Set<Integer> distinctelements = new HashSet<Integer>();
            for (int j : arr) {
                distinctelements.add(j);
            }
            int number = distinctelements.size();
            if(number > k) {
                out.println(-1);
            } else {
                Object[] new_arr = distinctelements.toArray();
                int[] overall_arr = new int[k];
                for(int j=0; j<k; j++) {
                    if(j<number) {
                        overall_arr[j] = (int) new_arr[j];
                    } else {
                        overall_arr[j] = 1;
                    }
                }
                out.println(n*k);
                for(int j=0; j<n; j++) {
                    for(int x=0; x<k; x++) {
                        out.println(overall_arr[x]);
                    }
                }
            }

        }
        




      
      

      
      
      
      
      
      // Start writing your solution here. -------------------------------------
   
      /*
      int n      = sc.nextInt();        // read input as integer
      long k     = sc.nextLong();       // read input as long
      double d   = sc.nextDouble();     // read input as double
      String str = sc.next();           // read input as String
      String s   = sc.nextLine();       // read whole line as String

      int result = 3*n;
      out.println(result);                    // print via PrintWriter
      */

      // Stop writing your solution here. -------------------------------------
    out.close();
   }

 static  class pair{
    int u;
    int v;
    int w;
    pair(int u, int v, int w) {
        this.u=u;
        this.v=v;
        this.w=w;
    }
    
}

static class sortbyarr implements Comparator<pair> 
{ 
    // Used for sorting in ascending order of 
    // roll number 
    public int compare(pair a, pair b) 
    { 
        return a.u - b.u; 
    } 
}

static class sortbyi implements Comparator<pair> 
{ 
    // Used for sorting in ascending order of 
    // roll number 
    public int compare(pair a, pair b) 
    { 
        return a.v - b.v; 
    } 
}



   //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }

   }
   //--------------------------------------------------------
}