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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.List;
import java.util.Objects;
import java.util.Random;
import java.util.Set;
import java.util.StringTokenizer;

public class B {

  static MyScanner scanner = new MyScanner();
  static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
  static final int MOD = 1000000007;
  static final boolean oj = System.getProperty("ONLINE_JUDGE") != null;
  static final int[][] d4 = new int[][]{{-1, 0}, {0, -1}, {1, 0}, {0, 1}};
  static final int[][] d8 = new int[][]{{-1, -1}, {-1, 0}, {-1, 1}, {0, -1}, {0, 1}, {1, -1}, {1, 0}, {1, 1}};
  static final int N = 0;

  public static void main(String[] args) {
    int tc = scanner.nextInt();
    for(int t=0; t<tc; t++) {
      int n = scanner.nextInt();
      int k = scanner.nextInt();
      int[] a = new int[n];
      Set<Integer> s = new HashSet<>();
      for(int i=0; i<n; i++) {
        a[i] = scanner.nextInt();
        s.add(a[i]);
      }
      if(s.size() > k) {
        out.println(-1);
        continue;
      }
      List<Integer> res = new ArrayList<>(s);
      int i = 0, ci = 0;
      while(i < n) {
        if(res.size() < k) {
          res.add(a[i]);
          i++;
        } else {
          res.add(res.get(ci));
          if (res.get(ci) == a[i]) {
            i++;
          }
          ci++;
        }
      }
      out.println(res.size());
      for(int j=0; j<res.size(); j++) {
        if(j > 0) out.print(' ');
        out.print(res.get(j));
      }
      out.println();
    }
    out.close();
  }

  public static void print(Object o) {
    if(!oj) {
      out.println(o);
    }
  }

  //Find the GCD of two numbers
  public static long gcd(long a, long b) {
    if (a < b) return gcd(b,a);
    if (b == 0)
      return a;
    else
      return gcd(b,a%b);
  }

  private static long[] fac = new long[N+1];
  private static long[] invfac = new long[N+1];

  private static long fac(int n){
    if(n == 0) return fac[0] = 1;
    else if(fac[n] > 0) return fac[n];
    else return fac[n] = n * fac(n-1) % MOD;
  }

  private static long invfac(int n){
    if(invfac[n] > 0) return invfac[n];
    else return invfac[n] = inv(fac[n]);
  }

  private static long choose(int n, int k){
    return fac(n) * invfac(k) % MOD * invfac(n-k) % MOD;
  }

  private static long inv(long a){
    return (gcdex(a, MOD).key + MOD) % MOD;
  }

  private static Pair<Long, Long> gcdex(long a, long b){
    if(b > a) return gcdex(b, a).invert();
    else if(b == 0) return new Pair<>(1L, 0L);
    else{
      Pair<Long, Long> p = gcdex(b, a % b);
      return new Pair<>(p.key, p.key - p.value*(a/b));
    }
  }

  //Fast exponentiation (x^y mod m)
  public static long power(long x, long y, long m) {
    if (y < 0) return 0L;
    long ans = 1;
    x %= m;
    while (y > 0) {
      if(y % 2 == 1)
        ans = (ans * x) % m;
      y /= 2;
      x = (x * x) % m;
    }
    return ans;
  }

  public static int[] shuffle(int[] array) {
    Random rgen = new Random();
    for (int i = 0; i < array.length; i++) {
      int randomPosition = rgen.nextInt(array.length);
      int temp = array[i];
      array[i] = array[randomPosition];
      array[randomPosition] = temp;
    }
    return array;
  }

  public static long[] shuffle(long[] array) {
    Random rgen = new Random();
    for (int i = 0; i < array.length; i++) {
      int randomPosition = rgen.nextInt(array.length);
      long temp = array[i];
      array[i] = array[randomPosition];
      array[randomPosition] = temp;
    }
    return array;
  }

  public static int[][] shuffle(int[][] array) {
    Random rgen = new Random();
    for (int i = 0; i < array.length; i++) {
      int randomPosition = rgen.nextInt(array.length);
      int[] temp = array[i];
      array[i] = array[randomPosition];
      array[randomPosition] = temp;
    }
    return array;
  }

  public static int[][] sort(int[][] array) {
    //Sort an array (immune to quicksort TLE)

    Arrays.sort(array, new Comparator<int[]>() {
      @Override
      public int compare(int[] a, int[] b) {
        return a[1]-b[1]; //ascending order
      }
    });
    return array;
  }

  public static long[][] sort(long[][] array) {
    //Sort an array (immune to quicksort TLE)
    Random rgen = new Random();
    for (int i = 0; i < array.length; i++) {
      int randomPosition = rgen.nextInt(array.length);
      long[] temp = array[i];
      array[i] = array[randomPosition];
      array[randomPosition] = temp;
    }
    Arrays.sort(array, new Comparator<long[]>() {
      @Override
      public int compare(long[] a, long[] b) {
        if (a[0] < b[0])
          return -1;
        else if (a[0] > b[0])
          return 1;
        else
          return 0;
      }
    });
    return array;
  }

  static class MyScanner {
    private BufferedReader br;
    private StringTokenizer st;

    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;
    }
  }

  static class Pair<K,V> {

    public K key;
    public V value;

    public Pair(K key, V value) {
      this.key = key;
      this.value = value;
    }

    @Override
    public String toString() {
      return key + ":" + value;
    }

    @Override
    public int hashCode() {
      return key.hashCode() * 13 + (value == null ? 0 : value.hashCode());
    }

    @Override
    public boolean equals(Object o) {
      if (this == o) return true;
      if (o instanceof Pair) {
        Pair pair = (Pair) o;
        return Objects.equals(key, pair.key) && Objects.equals(value, pair.value);
      }
      return false;
    }

    public Pair<V, K> invert() {
      return new Pair<>(value, key);
    }
  }

  static class Triple<A, B, C> {
    public A a;
    public B b;
    public C c;

    public Triple(A a, B b, C c) {
      this.a = a;
      this.b = b;
      this.c = c;
    }

    @Override
    public String toString() {
      return a + ":" + b + ":" + c;
    }

    @Override
    public int hashCode() {
      return (a == null ? 0 : a.hashCode()) * 13 + (b == null ? 0 : b.hashCode()) * 41 + (c == null ? 0 : c.hashCode());
    }

    @Override
    public boolean equals(Object o) {
      if (this == o) return true;
      if (o instanceof Triple) {
        Triple triple = (Triple) o;
        return Objects.equals(a, triple.a) && Objects.equals(b, triple.b) && Objects.equals(c, triple.c);
      }
      return false;
    }
  }
}