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.Writer;
import java.io.BufferedWriter;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.*;
import java.io.*;
import java.math.*;

public class B{
  static class ProblemSolver{
    public void solveTheProblem(InputReader in,OutputWriter out, NumberTheory nt){
      int test=in.nextInt();
      while(test-- >0){
        int n=in.nextInt();
        int k=in.nextInt();
        ArrayList<Integer> ar= new ArrayList<>();
        int max=-1;
        HashSet<Integer> fr= new HashSet<>();
        for(int i=0;i<n;i++){
          int temp=in.nextInt();
          max=Math.max(max, temp);
          fr.add(temp);
          ar.add(temp);
        }
        if(k<fr.size()){
          System.out.println(-1);
          continue;
        }
        System.out.println(n*k);
        for(int i=0;i<n;i++){
          for(int ii: fr)
            System.out.print(ii+" ");
          for(int ii=0;ii<k-fr.size();ii++)
            System.out.print(1+" ");

        }
        System.out.println();
      }
    }
  }

  public static void main(String[] args){
    InputStream inputStream=System.in;
    OutputStream outputStream=System.out;
    InputReader in=new InputReader(inputStream);
    OutputWriter out=new OutputWriter(outputStream);
    NumberTheory nt= new NumberTheory();
    ProblemSolver problemSolver=new ProblemSolver();
    problemSolver.solveTheProblem(in,out, nt);
    out.flush();
    out.close();
  }



  static class InputReader {
    private boolean finished = false;

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public InputReader(InputStream stream) {
      this.stream = stream;
    }

    public int read() {
      if (numChars == -1) {
        throw new InputMismatchException();
      }
      if (curChar >= numChars) {
        curChar = 0;
        try {
          numChars = stream.read(buf);
        } catch (IOException e) {
          throw new InputMismatchException();
        }
        if (numChars <= 0) {
          return -1;
        }
      }
      return buf[curChar++];
    }

    public int peek() {
      if (numChars == -1) {
        return -1;
      }
      if (curChar >= numChars) {
        curChar = 0;
        try {
          numChars = stream.read(buf);
        } catch (IOException e) {
          return -1;
        }
        if (numChars <= 0) {
          return -1;
        }
      }
      return buf[curChar];
    }

    public int nextInt() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      int res = 0;
      do {
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c - '0';
        c = read();
      } while (!isSpaceChar(c));
      return res * sgn;
    }

    public long nextLong() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      long res = 0;
      do {
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c - '0';
        c = read();
      } while (!isSpaceChar(c));
      return res * sgn;
    }

    public String nextLine() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      StringBuilder res = new StringBuilder();
      do {
        if (Character.isValidCodePoint(c)) {
          res.appendCodePoint(c);
        }
        c = read();
      } while (!isSpaceChar(c));
      return res.toString();
    }

    public boolean isSpaceChar(int c) {
      if (filter != null) {
        return filter.isSpaceChar(c);
      }
      return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private String readLine0() {
      StringBuilder buf = new StringBuilder();
      int c = read();
      while (c != '\n' && c != -1) {
        if (c != '\r') {
          buf.appendCodePoint(c);
        }
        c = read();
      }
      return buf.toString();
    }

    public String readLine() {
      String s = readLine0();
      while (s.trim().length() == 0) {
        s = readLine0();
      }
      return s;
    }

    public String readLine(boolean ignoreEmptyLines) {
      if (ignoreEmptyLines) {
        return readLine();
      } else {
        return readLine0();
      }
    }

    public BigInteger readBigInteger() {
      try {
        return new BigInteger(nextLine());
      } catch (NumberFormatException e) {
        throw new InputMismatchException();
      }
    }

    public char nextCharacter() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      return (char) c;
    }

    public double nextDouble() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      double res = 0;
      while (!isSpaceChar(c) && c != '.') {
        if (c == 'e' || c == 'E') {
          return res * Math.pow(10, nextInt());
        }
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c - '0';
        c = read();
      }
      if (c == '.') {
        c = read();
        double m = 1;
        while (!isSpaceChar(c)) {
          if (c == 'e' || c == 'E') {
            return res * Math.pow(10, nextInt());
          }
          if (c < '0' || c > '9') {
            throw new InputMismatchException();
          }
          m /= 10;
          res += (c - '0') * m;
          c = read();
        }
      }
      return res * sgn;
    }

    public boolean isExhausted() {
      int value;
      while (isSpaceChar(value = peek()) && value != -1) {
        read();
      }
      return value == -1;
    }

    public String next() {
      return nextLine();
    }

    public SpaceCharFilter getFilter() {
      return filter;
    }

    public void setFilter(SpaceCharFilter filter) {
      this.filter = filter;
    }

    public interface SpaceCharFilter {
      public boolean isSpaceChar(int ch);
    }
    public int[] nextIntArray(int n){
      int[] array=new int[n];
      for(int i=0;i<n;++i)array[i]=nextInt();
      return array;
    }
    public int[] nextSortedIntArray(int n){
      int array[]=nextIntArray(n);
      Arrays.sort(array);
      return array;
    }
    public ArrayList<Integer> nextIntArrayList(int n){
      ArrayList<Integer> ar= new ArrayList<>();
      for(int i=0;i<n;i++)
        ar.add(nextInt());
      return ar;
    }
		public ArrayList<Long> nextLongArrayList(int n){
      ArrayList<Long> ar= new ArrayList<>();
      for(int i=0;i<n;i++)
        ar.add(nextLong());
      return ar;
    }

    public int[] nextSumIntArray(int n){
      int[] array=new int[n];
      array[0]=nextInt();
      for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
      return array;
    }
    public long[] nextLongArray(int n){
      long[] array=new long[n];
      for(int i=0;i<n;++i)array[i]=nextLong();
      return array;
    }
    public long[] nextSumLongArray(int n){
      long[] array=new long[n];
      array[0]=nextInt();
      for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
      return array;
    }
    public long[] nextSortedLongArray(int n){
      long array[]=nextLongArray(n);
      Arrays.sort(array);
      return array;
    }
    public int[][] nextIntMatrix(int n,int m){
      int[][] matrix=new int[n][m];
      for(int i=0;i<n;++i)
      for(int j=0;j<m;++j)
      matrix[i][j]=nextInt();
      return matrix;
    }

    public int[][] nextIntMatrix(int n){
      return nextIntMatrix(n,n);
    }

    public long[][] nextLongMatrix(int n,int m){
      long[][] matrix=new long[n][m];
      for(int i=0;i<n;++i)
      for(int j=0;j<m;++j)
      matrix[i][j]=nextLong();
      return matrix;
    }

    public long[][] nextLongMatrix(int n){
      return nextLongMatrix(n,n);
    }

    public char[][] nextCharMatrix(int n,int m){
      char[][] matrix=new char[n][m];
      for(int i=0;i<n;++i)
      matrix[i]=next().toCharArray();
      return matrix;
    }

    public char[][] nextCharMatrix(int n){
      return nextCharMatrix(n,n);
    }
  }

  static class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
      writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
      this.writer = new PrintWriter(writer);
    }

    // public void print(char[] array) {
    //     writer.print(array);
    // }

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void print(int[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(double[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(long[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(char[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(String[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(int[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(double[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(long[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(char[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(String[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void println(int[] array) {
      print(array);
      writer.println();
    }

    public void println(double[] array) {
      print(array);
      writer.println();
    }

    public void println(long[] array) {
      print(array);
      writer.println();
    }

    // public void println(char[] array) {
    //     print(array);
    //     writer.println();
    // }

    public void println(String[] array) {
      print(array);
      writer.println();
    }

    public void println() {
      writer.println();
    }

    public void println(Object... objects) {
      print(objects);
      writer.println();
    }

    public void print(char i) {
      writer.print(i);
    }

    public void println(char i) {
      writer.println(i);
    }

    public void println(char[] array) {
      writer.println(array);
    }

    public void printf(String format, Object... objects) {
      writer.printf(format, objects);
    }

    public void close() {
      writer.close();
    }

    public void flush() {
      writer.flush();
    }

    public void print(long i) {
      writer.print(i);
    }

    public void println(long i) {
      writer.println(i);
    }

    public void print(int i) {
      writer.print(i);
    }

    public void println(int i) {
      writer.println(i);
    }

    public void separateLines(int[] array) {
      for (int i : array) {
        println(i);
      }
    }
  }
  static class NumberTheory{

      /**
       * Modular Arithmetic:
       *  1. (a+b)%c=(a%c+b%c)%c
       *  2. (a*b)%c=(a%c*b%c)%c
       *  3. (a-b)%c=(a%c-b%c+c)%c
       *  4. (a/b)%c=(a%c*(b^-1)%c)%c -- (b^-1 is multiplicative modulo inverse)
       */
      //Modular Addition
      public int modularAddition(int a,int b,int MOD){
          return (a%MOD+b%MOD)%MOD;
      }
      public long modularAddition(long a,long b,long MOD){
          return (a%MOD+b%MOD)%MOD;
      }
      //Modular Multiplication
      public int modularMultiplication(int a,int b,int MOD){
          return ((a%MOD)*(b%MOD))%MOD;
      }
      public long modularMultiplication(long a,long b,long MOD){
          return ((a%MOD)*(b%MOD))%MOD;
      }
      //Modular Subtraction
      public int modularSubtraction(int a,int b,int MOD){
          return (a%MOD-b%MOD+MOD)%MOD;
      }
      public long modularSubtraction(long a,long b,long MOD){
          return (a%MOD-b%MOD+MOD)%MOD;
      }

      /**
       * Binary Exponentiation
       */
      public int binaryExponentiation(int x,int n){
          if(n==0)return 1;
          else if(n%2==0)return binaryExponentiation(x*x,n/2);
          else return x*binaryExponentiation(x*x,(n-1)/2);
      }
      public long binaryExponentiation(long x,long n){
          long result=1;
          while(n>0){
              if(n%2==1)result*=x;
              x=x*x;
              n/=2;
          }
          return result;
      }

      /**
       * Modular Exponentiation
       */
      public int modularExponentiation(int x,int n,int MOD){
          if(n==0)return 1%MOD;
          else if(n%2==0)return modularExponentiation(modularMultiplication(x,x,MOD),n/2,MOD);
          else return modularMultiplication(x,modularExponentiation(modularMultiplication(x,x,MOD),(n-1)/2,MOD),MOD);
      }
      public long modularExponentiation(long x,long n,long MOD){
          long result=1;
          while(n>0){
              if(n%2==1)result=modularMultiplication(result,x,MOD);
              x=modularMultiplication(x,x,MOD);
              n/=2;
          }
          return result;
      }

      /**
       * Factorial of a number
       */
      public long factorials(long n){
          if(n==0)return 1;
          return n*factorials(n-1);
      }

      /**
       * Prime factors of a number
       */
      public ArrayList<Integer> distinctPrimeFactors(int n){
          ArrayList<Integer> factorials=new ArrayList<>();
          int limit=(int)Math.sqrt(n);
          if(n%2==0){
              factorials.add(2);
              while(n%2==0)n/=2;
          }
          for(int i=3;i<=limit;i+=2){
              if(n%i==0){
                  factorials.add(i);
                  while(n%i==0)n/=i;
              }
          }
          if(n>2)factorials.add(n);
          return factorials;
      }

      public ArrayList<Long> distinctPrimeFactors(long n){
          ArrayList<Long> factorials=new ArrayList<>();
          long limit=(long)Math.sqrt(n);
          if(n%2==0){
              factorials.add((long)2);
              while(n%2==0)n/=2;
          }
          for(long i=3;i<=limit;i+=2){
              if(n%i==0){
                  factorials.add(i);
                  while(n%i==0)n/=i;
              }
          }
          if(n>2)factorials.add(n);
          return factorials;
      }

      public ArrayList<Integer> primeFactors(int n){
          ArrayList<Integer> factorials=new ArrayList<>();
          int limit=(int)Math.sqrt(n);
          if(n%2==0){
              factorials.add(2);
              while(n%2==0)n/=2;
          }
          for(int i=3;i<=limit;i+=2){
              if(n%i==0){
                  factorials.add(i);
                  while(n%i==0)n/=i;
              }
          }
          if(n>2)factorials.add(n);
          return factorials;
      }

      public ArrayList<Long> primeFactors(long n){
          ArrayList<Long> factorials=new ArrayList<>();
          long limit=(long)Math.sqrt(n);
          if(n%2==0){
              factorials.add((long)2);
              while(n%2==0)n/=2;
          }
          for(long i=3;i<=limit;i+=2){
              if(n%i==0){
                  factorials.add(i);
                  while(n%i==0)n/=i;
              }
          }
          if(n>2)factorials.add(n);
          return factorials;
      }

      /**
       * Combination: nCr
       */
      //Naive version
      //(n,r)=(n-1,r-1)+(n-1,r) for r!=0 or r!=n
      //(n,0)=(n,n)=1
      public int binomialCoefficientRecursive(int n,int k){
          if(k==0 || k==n)return 1;//base case
          return binomialCoefficientRecursive(n-1,k-1)+binomialCoefficientRecursive(n-1,k);//recursion
      }

      //Dynamic Programming version(Uses bottom up approach to fill the table)
      //Time complexity: O(n*k)
      //Space complexity: O(n*k)
      public long binomialCoefficientIterative(int n,int k){
          long[][] C=new long[n+1][k+1];
          for(int i=0;i<=n;++i){
              for(int j=0;j<=Math.min(n,k);++j){
                  if(j==0 || j==i)C[i][j]=1;
                  else C[i][j]=C[i-1][j-1]+C[i-1][j];
              }
          }
          return C[n][k];
      }

      //Pascal's Triangle version(Space efficient program)
      //Time complexity: O(n*k)
      //Space complexity: O(k)
      public long nCr(int n,int r){
          int[] C=new int[r+1];
          C[0]=1;//nC0=1
          for(int i=1;i<=n;++i)
              for(int j=Math.min(i,r);j>0;--j)
                  C[j]=C[j]+C[j-1];
          return C[r];
      }

      /**
       * Catlan number:
       *  - Time complexity: O(n*n)
       *  - Auxiliary space: O(n)
       *
       *  NOTE: Time complexity could be reduced to O(n) but it is
       *        possible if and only if n is small or else there is
       *        a chance of getting an overflow. To decrease the time
       *        complexity to O(n) just remember nCr=nCn-r
       */
      public long catlanNumber(int n){
          long[] catlan=new long[n+1];
          catlan[0]=catlan[1]=1;
          for(int i=2;i<=n;++i)
              for(int j=0;j<i;++j)
                  catlan[i]+=catlan[j]*catlan[i-1-j];

          return catlan[n];
      }

      /**
       * Greatest Common Divisor(GCD)
       *  - It is also known as Highest Common Factor(HCF)
       *  - Time complexity: log(min(a,b))
       *  - Auxiliary Space: O(1)
       */
      public int gcd(int a,int b){
          if(b==0)return a;
          return gcd(b,a %b);
      }

      public long gcd(long a,long b){
          if(b==0)return a;
          return gcd(b,a%b);
      }

      /**
       * Extended Euclid's Algorithm:
       *  - ax+by=gcd(a,b)
       *  - Time complexity:
       *  -
       */


      /**
       * Least Common Multiple(LCM):
       *  - Time complexity: log(min(a,b))
       *  - Auxiliary Space: O(1)
       */
      public long lcm(long a,long b){
          return (a*b)/gcd(a,b);
      }

  }
}
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//              "I8,      "I8      mI8I88"". . . . . .,m8"   "8
//               I8m,  __ ;I8   ,II88" . . . . .,;miI88"
//               "I88I8I88I88,,I88" . . . ,mmiiI8888"
//                ,I8". . ."I8I8". . . mi888888888"
//              ,I8 . . . .,I88I. . .i88888888888"
//             I8. . . .,mII88Ima. .i88888888888"
//            ,8"..,mI88I88I88I8Imi888888888888"
//            I8.,I8I"""        ""II88888888888
//           ;I8I8"                  ""I8888888
//           ""                         "I88888
//                                        "I888
//                                         "I88,
//                                          "I88
//                                           "88,
//                                            I88,              ______   __
//                           ______           "I88__        .mI88I88I88I88I88,
//                      .,mI88I88I88, ,mI88,   I88"""     ,mI8". . . . "I8,..8,
//                    ,I888' . . . "I88.\ "8,  I88      ,I8". . . .  / :;I8 \ 8,
//                  .mI8' . . .  / .:"I8.\ 88  "88,    ,8". . .  / .;mI8I8I8,\ 8
//                 ,I8'. . .  / . .:;,I8I8I888  I88   ,8". .  / .:mI8"'   "I8,:8
//                ,I8'. . . / . .:;,mI8"  `"I88 I88   I8. .  / .m8"         "I8I
//               ,I8 . .  / . .:;,mI8"      "I88888   88,.  / ,m8            "8'
//               I8'. .  / . .;,mI8"          "II888 ,I8I8,.,I8"
//               I8 . . / . .,mI8"              I8888888' """
//               `I8,.  / ;,mI8"                 II888
//                "I8I, /,mI8"                 __I888
//                  "I8888"                   """I88
//                    ""                         I88
//                                               I88__
//                                               I88"""
//                                               I88
//                                               I88
//                                             __I88
//                                            """I88
//                                               I88
//                                               I88
//                                               I88__
//                                               I88"""
//                                               I88
//                                        BITSY  ___  CHUCK