We have a sequence of N \times K integers: X=(X_0,X_1,\cdots,X_{N \times K-1}). Its elements are represented by another sequence of N integers: A=(A_0,A_1,\cdots,A_{N-1}). For each pair i, j (0 \leq i \leq K-1,\ 0 \leq j \leq N-1), X_{i \times N + j}=A_j holds.

Snuke has an integer sequence s, which is initially empty. For each i=0,1,2,\cdots,N \times K-1, in this order, he will perform the following operation:

* If s does not contain X_i: add X_i to the end of s.
* If s does contain X_i: repeatedly delete the element at the end of s until s no longer contains X_i. Note that, in this case, we do not add X_i to the end of s.



Find the elements of s after Snuke finished the operations.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq K \leq 10^{12}
* 1 \leq A_i \leq 2 \times 10^5
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
A_0 A_1 \cdots A_{N-1}


Output

Print the elements of s after Snuke finished the operations, in order from beginning to end, with spaces in between.

Examples

Input

3 2
1 2 3


Output

2 3


Input

5 10
1 2 3 2 3


Output

3


Input

6 1000000000000
1 1 2 2 3 3


Output




Input

11 97
3 1 4 1 5 9 2 6 5 3 5


Output

9 2 6
import java.io.*;
import java.nio.CharBuffer;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.NoSuchElementException;

public class Main {

    private static final int MAX = 200000;

    public static void main(String[] args) {
        SimpleScanner scanner = new SimpleScanner(System.in);
        PrintWriter writer = new PrintWriter(System.out);

        int n = scanner.nextInt();
        long k = scanner.nextLong();
        int[] a = new int[n];
        int[] first = new int[MAX + 1];
        Arrays.fill(first, -1);
        for (int i = 0; i < n; ++i) {
            a[i] = scanner.nextInt();
            if (first[a[i]] < 0)
                first[a[i]] = i;
        }
        int[] right = new int[MAX + 1];
        Arrays.fill(right, -1);
        int[] jump = new int[n];
        int[] roundAdd = new int[n];
        for (int i = n - 1; i >= 0; --i) {
            if (right[a[i]] < 0) {
                jump[i] = (first[a[i]] + 1) % n;
                roundAdd[i] = 1;
            } else {
                jump[i] = (right[a[i]] + 1) % n;
            }
            right[a[i]] = i;
        }
//        writer.println(Arrays.toString(jump));
        int p = 0;
        int round = 0;
        ArrayList<Integer> roundStart = new ArrayList<>(n + 1);
        int loopSize = 0;
        while (true) {
            if (roundStart.size() == round)
                roundStart.add(p);
            round += roundAdd[p];
            if (jump[p] == 0) {
                loopSize = round + 1;
                break;
            }
            p = jump[p];
        }
//        writer.println(loopSize);
//        writer.println(roundStart);
        --k;
        if (roundStart.size() > k % loopSize) {
            boolean[] flag = new boolean[MAX + 1];
            LinkedList<Integer> ans = new LinkedList<>();
            for (int i = roundStart.get((int) (k % loopSize)); i < n; ++i) {
                if (flag[a[i]]) {
                    do {
                        int t = ans.pollLast();
                        flag[t] = false;
                    } while (flag[a[i]]);
                } else {
                    ans.offerLast(a[i]);
                    flag[a[i]] = true;
                }
            }
            for (int x : ans) {
                writer.print(x + " ");
            }
            writer.println();
        }
        writer.close();
    }

    private static class SimpleScanner {

        private static final int BUFFER_SIZE = 10240;

        private Readable in;
        private CharBuffer buffer;
        private boolean eof;

        SimpleScanner(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
            buffer = CharBuffer.allocate(BUFFER_SIZE);
            buffer.limit(0);
            eof = false;
        }


        private char read() {
            if (!buffer.hasRemaining()) {
                buffer.clear();
                int n;
                try {
                    n = in.read(buffer);
                } catch (IOException e) {
                    n = -1;
                }
                if (n <= 0) {
                    eof = true;
                    return '\0';
                }
                buffer.flip();
            }
            return buffer.get();
        }

        void checkEof() {
            if (eof)
                throw new NoSuchElementException();
        }

        char nextChar() {
            checkEof();
            char b = read();
            checkEof();
            return b;
        }

        String next() {
            char b;
            do {
                b = read();
                checkEof();
            } while (Character.isWhitespace(b));
            StringBuilder sb = new StringBuilder();
            do {
                sb.append(b);
                b = read();
            } while (!eof && !Character.isWhitespace(b));
            return sb.toString();
        }

        int nextInt() {
            return Integer.valueOf(next());
        }

        long nextLong() {
            return Long.valueOf(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}