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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
//import java.math.BigInteger;
import java.util.*;

public class AAA1 {
    public static void main(String[] args) {
        handmadeInput.FastReader in = new handmadeInput.FastReader();
        int t = in.nextInt();
        StringBuilder s=new StringBuilder();
        while (t-- > 0) {
            int n = in.nextInt();
            int k = in.nextInt();
            HashSet<Integer> list = new HashSet<>(n);
            for (int i = 0; i < n; i++) {
                list.add(in.nextInt());
            }
            if(list.size()>k){
                s.append("-1").append(" ");
            }
            else{
s.append(n*k).append(" ");
                for(int i=0;i<n;i++){
                    for(int j:list){
                        s.append(j).append(" ");
                    }
                    for(int j=0;j<k-list.size();j++){
                        s.append("1").append(" ");
                    }
                }
            }
            

        }
        System.out.println(s);

    }
}




// Additional Classes go here



class handmadeInput {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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;
        }
    }
}

class UtilityFunctions {
    //! returns gcd of given numbers
   public int gcd(int a, int b)
    {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

 public int primeFactors(int n) {
        HashMap<Integer, Integer> hashMap = new HashMap<>(n);
        int c = 0;

        // Print the number of 2s that divide n
        while (n % 2 == 0) {
//            if (hashMap.containsKey(2)) {
//                hashMap.replace(2, hashMap.get(2) + 1);
//            } else {
//                hashMap.put(2, 1);
//            }
            c++;
            n /= 2;
        }

        // n must be odd at this point.  So we can
        // skip one element (Note i = i +2)
        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            // While i divides n, print i and divide n
            while (n % i == 0) {
                //System.out.print(i + " ");

//                if (hashMap.containsKey(i)) {
//                    hashMap.replace(i, hashMap.get(i) + 1);
//                } else {
//                    hashMap.put(i, 1);
//                }
                c++;
                n /= i;
            }
        }

        // This condition is to handle the case whien
        // n is a prime number greater than 2
        if (n > 2) {

//            if (hashMap.containsKey(n)) {
//                hashMap.replace(n, hashMap.get(n) + 1);
//            } else {
//                hashMap.put(n, 1);
//            }
            c++;
        }

        //System.out.print(n);
        return c;
    }
}