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 {

    void solve() throws IOException {
        in = new InputReader("__std");
        out = new OutputWriter("__std");

        int testCount = in.readInt();
        for (int test = 1; test <= testCount; ++test) {
            int n = in.readInt();
            int k = in.readInt();
            int[] a = new int[n];
            boolean[] mask = new boolean[n];
            int distinct = 0;
            for (int i = 0; i < n; ++i) {
                a[i] = in.readInt() - 1;
                if (!mask[a[i]]) {
                    ++distinct;
                    mask[a[i]] = true;
                }
            }
            if (distinct > k) {
                out.println(-1);
                continue;
            }
            List<Integer> b = new ArrayList<>();
            for (int v = 0; v < n; ++v) {
                if (distinct < k && !mask[v]) {
                    ++distinct;
                    mask[v] = true;
                }
                if (mask[v]) {
                    b.add(v);
                }
            }
            int left = 0;
            for (int i = 0; i < n; ++i) {
                while (b.get(left) != a[i]) {
                    b.add(b.get(left));
                    ++left;
                }
                b.add(a[i]);
                ++left;
            }
            out.println(b.size());
            for (int v : b) {
                out.print((v + 1) + " ");
            }
            out.println();
        }

        exit();
    }

    void exit() {
        out.close();
        //System.err.println((System.currentTimeMillis() - startTime) + " ms");
        System.exit(0);
    }

    InputReader in;
    OutputWriter out;

    //long startTime = System.currentTimeMillis();

    public static void main(String[] args) throws IOException {
        new B().solve();
    }

    class InputReader {

        private InputStream stream;

        private byte[] buffer = new byte[1024];
        private int pos, len;

        private int cur;

        private StringBuilder sb = new StringBuilder(32);

        InputReader(String name) throws IOException {
            if (name.equals("__std")) {
                stream = System.in;
            } else {
                stream = new FileInputStream(name);
            }
            cur = read();
        }

        private int read() throws IOException {
            if (len == -1) {
                throw new EOFException();
            }
            if (pos >= len) {
                pos = 0;
                len = stream.read(buffer);
                if (len == -1) return -1;
            }
            return buffer[pos++] & 0xff;
        }

        boolean whitespace() {
            return cur == ' ' || cur == '\t' || cur == '\r' || cur == '\n' || cur == -1;
        }

        boolean eol() {
            return cur == '\r' || cur == '\n' || cur == -1;
        }

        boolean eof() {
            return cur == -1;
        }

        byte readByte() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            byte res = (byte) cur;
            cur = read();
            return res;
        }

        char readChar() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            char res = (char) cur;
            cur = read();
            return res;
        }

        int readInt() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            while (whitespace()) {
                cur = read();
            }
            if (eof()) {
                throw new EOFException();
            }
            int sign = 1;
            if (cur == '-') {
                sign = -1;
                cur = read();
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
            }
            int res = 0;
            while (!whitespace()) {
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
                res *= 10;
                res += cur - '0';
                cur = read();
            }
            return res * sign;
        }

        long readLong() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            while (whitespace()) {
                cur = read();
            }
            if (eof()) {
                throw new EOFException();
            }
            int sign = 1;
            if (cur == '-') {
                sign = -1;
                cur = read();
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
            }
            long res = 0;
            while (!whitespace()) {
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
                res *= 10;
                res += cur - '0';
                cur = read();
            }
            return res * sign;
        }

        double readDouble() throws IOException {
            return Double.parseDouble(readToken());
        }

        String readToken() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            while (whitespace()) {
                cur = read();
            }
            if (eof()) {
                throw new EOFException();
            }
            sb.setLength(0);
            while (!whitespace()) {
                sb.append((char) cur);
                cur = read();
            }
            return sb.toString();
        }

        String readLine() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            sb.setLength(0);
            while (!eol()) {
                sb.append((char) cur);
                cur = read();
            }
            if (cur == '\r') {
                cur = read();
            }
            if (cur == '\n') {
                cur = read();
            }
            return sb.toString();
        }

        void skipLine() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            while (!eol()) {
                cur = read();
            }
            if (cur == '\r') {
                cur = read();
            }
            if (cur == '\n') {
                cur = read();
            }
        }
    }

    class OutputWriter {

        private PrintWriter writer;

        OutputWriter(String name) throws IOException {
            if (name.equals("__std")) {
                writer = new PrintWriter(System.out);
            } else {
                writer = new PrintWriter(name);
            }
        }

        void print(String format, Object ... args) {
            writer.print(new Formatter(Locale.US).format(format, args));
        }

        void println(String format, Object ... args) {
            writer.println(new Formatter(Locale.US).format(format, args));
        }

        void print(Object value) {
            writer.print(value);
        }

        void println(Object value) {
            writer.println(value);
        }

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

        void printArray(int[] a) {
            boolean first = true;
            for (int v : a) {
                if (!first) {
                    writer.print(' ');
                } else {
                    first = false;
                }
                writer.print(v);
            }
            writer.println();
        }

        void printArray(int[][] a) {
            for (int[] v : a) {
                printArray(v);
            }
        }

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

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