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 javax.swing.*;
	import java.io.BufferedReader;
	import java.io.IOException;
	import java.io.InputStream;
	import java.io.InputStreamReader;
	import java.io.PrintWriter;
	import java.lang.reflect.Array;
	import java.util.*;
	 
	 
	public class Solution implements Runnable {
	 
	 
	    public void run() {
	 
	        InputReader input = new InputReader(System.in);
	        PrintWriter w = new PrintWriter(System.out);
	        
	        int t1 =input.nextInt();
	        
	        while(t1-->0)
	        {
	            int n=input.nextInt();
	            int k=input.nextInt();

	            int arr[]=new int[n];
	            for(int i=0;i<n;i++)
	                arr[i]=input.nextInt();
	            TreeSet<Integer> s=new TreeSet<>();
	            for(int i=0;i<n;i++)
	                s.add(arr[i]);

	            
	            if(s.size()>k)
	            {
	                System.out.println(-1);
	            }
	            else
	            {
	            for(int i=1;i<=n && s.size()<k;i++)
	            {
	                if(!s.contains(i))
	                {
	                    s.add(i);
	                }
	            }

	            Set<Integer> temp1=s.descendingSet();
	            ArrayList<Integer> ans=new ArrayList<Integer>();
	            		
	            for(int temp :temp1)
	            	ans.add(temp);

	            ArrayList<Integer> ans1=new ArrayList<>();
	            int j=0;
	            int i=0;

	            while(j!=n)
	            {
	                if(i==ans.size())
	                {
	                    i=0;
	                }

	                if(arr[j]==ans.get(i))
	                {
	                    ans1.add(arr[j]);
	                    j++;
	                    i++;
	                }
	                else
	                {
	                    ans1.add(ans.get(i));
	                    i++;
	                }
	            }
	            System.out.println(ans1.size());
				for(int i1=0;i1<ans1.size();i1++)
					System.out.print(ans1.get(i1)+ " ");
				System.out.println();
	            }	
	        }
	        				
	        				
	        				
	        				
	        				
	        	}
	        	
	        	
	        	
	        	
	        
	        	
	        
	        		
	        		
	        		
	        
	       
	        
	    
	    
	   
	    
	    
	    	
	    
	    static void ans(int[][] arr)
	    {
	    	
	    	
	    }
	class Sorting implements Comparator<pair>
	{
		public int compare(pair one, pair two)
		{
			if(one.a>two.a)
				return 1;
			else if(one.a==two.a)
				return 0;
			else 
				return -1;
					
		}
	}
	class pair
	{
		int a;
		int b;
		
		pair(int a ,int b)
		{
			this.a=a;
			this.b=b;
		}
			
	}
	 
	    class Graph{
	        private final int v;
	        private List<List<Integer>> adj;
	        Graph(int v){
	            this.v = v;
	            adj = new ArrayList<>(v);
	            for(int i=0;i<v;i++){
	                adj.add(new LinkedList<>());
	            }
	        }
	        private void addEdge(int a,int b){
	            adj.get(a).add(b);
	        }
	        private boolean isCyclic()
	        {
	            boolean[] visited = new boolean[v];
	            boolean[] recStack = new boolean[v];
	            for (int i = 0; i < v; i++)
	                if (isCyclicUtil(i, visited, recStack))
	                    return true;
	 
	            return false;
	        }
	        private boolean isCyclicUtil(int i, boolean[] visited, boolean[] recStack)
	        {
	            if (recStack[i])
	                return true;
	            if (visited[i])
	                return false;
	            visited[i] = true;
	            recStack[i] = true;
	            List<Integer> children = adj.get(i);
	            for (Integer c: children)
	                if (isCyclicUtil(c, visited, recStack))
	                    return true;
	            recStack[i] = false;
	            return false;
	        }
	    }
	    public static void sortbyColumn(int arr[][], int col)
	    {
	 
	        Arrays.sort(arr, new Comparator<int[]>()
	        {
	            public int compare(int[] o1, int[] o2){
	                return(Integer.valueOf(o1[col]).compareTo(o2[col]));
	            }
	        });
	 
	    }
	    static long gcd(long a, long b)
	    {
	        if (b == 0)
	            return a;
	        return gcd(b, a % b);
	    }
	    public static class DJSet {
	        public int[] upper;
	 
	        public DJSet(int n) {
	            upper = new int[n];
	            Arrays.fill(upper, -1);
	        }
	 
	        public int root(int x) {
	            return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
	        }
	 
	        public boolean equiv(int x, int y) {
	            return root(x) == root(y);
	        }
	 
	        public boolean union(int x, int y) {
	            x = root(x);
	            y = root(y);
	            if (x != y) {
	                if (upper[y] < upper[x]) {
	                    int d = x;
	                    x = y;
	                    y = d;
	                }
	                upper[x] += upper[y];
	                upper[y] = x;
	            }
	            return x == y;
	        }
	    }
	    public static int[] radixSort(int[] f)
	    {
	        int[] to = new int[f.length];
	        {
	            int[] b = new int[65537];
	            for(int i = 0;i < f.length;i++)b[1+(f[i]&0xffff)]++;
	            for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
	            for(int i = 0;i < f.length;i++)to[b[f[i]&0xffff]++] = f[i];
	            int[] d = f; f = to;to = d;
	        }
	        {
	            int[] b = new int[65537];
	            for(int i = 0;i < f.length;i++)b[1+(f[i]>>>16)]++;
	            for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
	            for(int i = 0;i < f.length;i++)to[b[f[i]>>>16]++] = f[i];
	            int[] d = f; f = to;to = d;
	        }
	        return f;
	    }
	    static class InputReader {
	        private InputStream stream;
	        private byte[] buf = new byte[1024];
	        private int curChar;
	        private int numChars;
	        private SpaceCharFilter filter;
	        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	 
	        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 String nextLine() {
	            String str = "";
	            try {
	                str = br.readLine();
	            }
	            catch (IOException e) {
	                e.printStackTrace();
	            }
	            return str;
	        }
	        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 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 String readString() {
	            int c = read();
	            while (isSpaceChar(c))
	                c = read();
	            StringBuilder res = new StringBuilder();
	            do {
	                res.appendCodePoint(c);
	                c = read();
	            }
	            while (!isSpaceChar(c));
	 
	            return res.toString();
	        }
	 
	        public boolean isSpaceChar(int c) {
	            if (filter != null)
	                return filter.isSpaceChar(c);
	            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	        }
	 
	        public String next() {
	            return readString();
	        }
	 
	        public interface SpaceCharFilter {
	            public boolean isSpaceChar(int ch);
	        }
	    }
	    public static void main(String args[]) throws Exception {
	        new Thread(null, new Solution(),"TaskA",1<<26).start();
	    }
	}