Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3 2
1 2 3

Sample Output 1

2 3

In this case, X=(1,2,3,1,2,3).
We will perform the operations as follows:

i=0: s does not contain 1, so we add 1 to the end of s, resulting in s=(1).

i=1: s does not contain 2, so we add 2 to the end of s, resulting in s=(1,2).

i=2: s does not contain 3, so we add 3 to the end of s, resulting in s=(1,2,3).

i=3: s does contain 1, so we repeatedly delete the element at the end of s as long as s contains 1, which causes the following changes to s: (1,2,3)→(1,2)→(1)→().

i=4: s does not contain 2, so we add 2 to the end of s, resulting in s=(2).

i=5: s does not contain 3, so we add 3 to the end of s, resulting in s=(2,3).

Sample Input 2

5 10
1 2 3 2 3

Sample Output 2

3

Sample Input 3

6 1000000000000
1 1 2 2 3 3

Sample Output 3

s may be empty in the end.

Sample Input 4

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

Sample Output 4

9 2 6

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func main() {
	var n, k int
	fmt.Scan(&n, &k)

	as := make([]int, n)
	var sc = bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	for i := range as {
		sc.Scan()
		as[i], _ = strconv.Atoi(sc.Text())
	}

	m := make(map[int]int)
	to := make([]int, n*2)
	for i := 0; i < n*2; i++ {
		v := as[i%n]
		if b, ok := m[v]; ok && b > -1 {
			to[b] = i - b
			m[v] = i
		} else {
			m[v] = i
		}
	}
	//fmt.Println("to: ", to)

	var i, j int
	//fmt.Println("i,j: ", i, j)
	for i := 0; i != k-1 || j+to[j]+1 < n; {
		j += (to[j] + 1)
		if j >= n {
			i++
			j %= n
		}
		//fmt.Println("i,j: ", i, j)
		if j == 0 {
			k = k % i
			i = 0
		}
	}

	var s []int
	m = make(map[int]int)
	for ; i < k; i++ {
		for ; j < n; j++ {
			if b, ok := m[as[j]]; ok && b > -1 {
				for l := len(s) - 1; s[l] != as[j]; l-- {
					m[s[l]] = -1
				}
				m[as[j]] = -1
				s = s[0:b]
			} else {
				s = append(s, as[j])
				m[as[j]] = len(s) - 1
			}
		}
	}

	for i := range s {
		if i == len(s)-1 {
			fmt.Println(s[i])
		} else {
			fmt.Printf("%d ", s[i])
		}
	}
}