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 Solution {

    private static BufferedReader br;
    private static StreamTokenizer st;
    private static PrintWriter pw;

    static final int INF = 1000000007;
    static final int MOD = 998244353;

    static List<Integer> edges[];

    static void bfs(int r, int dst[]) {
        Queue<Integer> queue = new LinkedList<>();
        boolean vis[] = new boolean[dst.length];
        vis[r] = true;
        dst[r] = 0;
        queue.offer(r);
        while (!queue.isEmpty()) {
            int x = queue.size();
            while (x-- > 0) {
                int f = queue.poll();
                List<Integer> es = edges[f];
                for (int i = 0; i < es.size(); i++) {
                    int t = es.get(i);
                    if (vis[t]) {
                        continue;
                    }
                    vis[t] = true;
                    dst[t] = dst[f] + 1;
                    queue.offer(t);
                }
            }
        }
    }

    static long count(long b, long lcm, long n) {
        long x = lcm - b;
        return n / lcm * x + Math.max(0, n % lcm - b + 1);
    }

    private static void solve() throws IOException {
        int tt = nextInt();
        for (int cs = 1; cs <= tt; cs++) {
            int n = nextInt();
            int k = nextInt();
            int a[] = new int[n];
            Set<Integer> cnt = new HashSet<>();
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
                cnt.add(a[i]);
            }
            boolean ok = true;
            if (cnt.size() > k) {
                ok = false;
            }
            List<Integer> rs = new ArrayList<>();
            if (k == n && ok) {
                for (int v : a) {
                    rs.add(v);
                }
            } else if (ok) {
                rs.addAll(cnt);
                for (int i = cnt.size() + 1; i <= k; i++) {
                    rs.add(1);
                }
                for (int i = 1; i < n; i++) {
                    for (int j = 0; j < k; j++) {
                        rs.add(rs.get(rs.size() - k));
                    }
                }
            }

            if (ok) {
                pw.println(rs.size());
                for (int i = 0; i < rs.size(); i++) {
                    if (i > 0) {
                        pw.print(" ");
                    }
                    pw.print(rs.get(i));
                }
            } else {
                pw.print(-1);
            }
//            pw.format("Case #%d: %f", cs, 1.0 - del);
            if (cs < tt) {
                pw.println();
            }
        }
//        int n = nextInt();
    }

    static void getDiv(Map<Integer, Integer> map, int n) {
        int sqrt = (int) Math.sqrt(n);
        for (int i = sqrt; i >= 2; i--) {
            if (n % i == 0) {
                getDiv(map, i);
                getDiv(map, n / i);
                return;
            }
        }
        map.put(n, map.getOrDefault(n, 0) + 1);
    }

    public static boolean[] generatePrime(int n) {
        boolean p[] = new boolean[n + 1];
        p[2] = true;

        for (int i = 3; i <= n; i += 2) {
            p[i] = true;
        }

        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            if (!p[i]) {
                continue;
            }
            for (int j = i * i; j <= n; j += i << 1) {
                p[j] = false;
            }
        }
        return p;
    }

    static boolean isPrime(long n) { //determines if n is a prime number
        int p[] = {2, 3, 5, 233, 331};
        int pn = p.length;
        long s = 0, t = n - 1;//n - 1 = 2^s * t
        while ((t & 1) == 0) {
            t >>= 1;
            ++s;
        }
        for (int i = 0; i < pn; ++i) {
            if (n == p[i]) {
                return true;
            }
            long pt = pow(p[i], t, n);
            for (int j = 0; j < s; ++j) {
                long cur = llMod(pt, pt, n);
                if (cur == 1 && pt != 1 && pt != n - 1) {
                    return false;
                }
                pt = cur;
            }
            if (pt != 1) {
                return false;
            }
        }
        return true;
    }

    static long llMod(long a, long b, long mod) {
        return (a * b - (long) ((double) a / mod * b + 0.5) * mod + mod) % mod;
//        long r = 0;
//        a %= mod;
//        b %= mod;
//        while (b > 0) {
//            if ((b & 1) == 1) {
//                r = (r + a) % mod;
//            }
//            b >>= 1;
//            a = (a << 1) % mod;
//        }
//        return r;
    }

    static int pow(long a, long n) {
        long ans = 1;
        while (n > 0) {
            if ((n & 1) == 1) {
                ans = (ans * a) % MOD;
            }
            a = (a * a) % MOD;
            n >>= 1;
        }
        return (int) ans;
    }

    static int pow(long a, long n, long mod) {
        long ans = 1;
        while (n > 0) {
            if ((n & 1) == 1) {
                ans = llMod(ans, a, mod);
            }
            a = llMod(a, a, mod);
            n >>= 1;
        }
        return (int) ans;
    }

    private static long[][] initC(int n) {
        long c[][] = new long[n][n];

        for (int i = 0; i < n; i++) {
            c[i][0] = 1;
        }

        for (int i = 1; i < n; i++) {
            for (int j = 1; j <= i; j++) {
                c[i][j] = c[i - 1][j - 1] + c[i - 1][j];
            }
        }
        return c;
    }

    /**
     * ps: n >= m, choose m from n;
     */
    private static int c(long n, long m) {
        if (m > n) {
            n ^= m;
            m ^= n;
            n ^= m;
        }
        m = Math.min(m, n - m);

        long top = 1;
        long bot = 1;
        for (long i = n - m + 1; i <= n; i++) {
            top = (top * i) % MOD;
        }
        for (int i = 1; i <= m; i++) {
            bot = (bot * i) % MOD;
        }

        return (int) ((top * pow(bot, MOD - 2)) % MOD);
    }

    static int gcd(int a, int b) {
        if (a < b) {
            return gcd(b, a);
        }
        while (b != 0) {
            int tmp = a % b;
            a = b;
            b = tmp;
        }
        return a;
    }

    static boolean even(long n) {
        return (n & 1) == 0;
    }

    public static void main(String args[]) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        st = new StreamTokenizer(br);
        pw = new PrintWriter(new OutputStreamWriter(System.out));
        st.ordinaryChar('\'');
        st.ordinaryChar('\"');
        st.ordinaryChar('/');

        long t = System.currentTimeMillis();
        solve();
        pw.flush();
    }

    private static long[] anLong(int n) throws IOException {
        long a[] = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    private static String next(int len) throws IOException {
        char ch[] = new char[len];
        int cur = 0;
        char c;
        while ((c = (char) br.read()) == '\n' || c == '\r' || c == ' ' || c == '\t') ;
        do {
            ch[cur++] = c;
        } while (!((c = (char) br.read()) == '\n' || c == '\r' || c == ' ' || c == '\t'));
        return String.valueOf(ch, 0, cur);
    }

    private static int nextInt() throws IOException {
        st.nextToken();
        return (int) st.nval;
    }

    private static long nextLong() throws IOException {
        st.nextToken();
        return (long) st.nval;
//        return Long.parseLong(nextLine());
    }

    private static double nextDouble() throws IOException {
        st.nextToken();
        return st.nval;
    }

    private static String[] nextSS(String reg) throws IOException {
        return br.readLine().split(reg);
    }

    private static String nextLine() throws IOException {
        return br.readLine();
    }
}