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 Kotlin (1.0.0) (judge verdict: Runtime Error)

import java.io.PrintWriter
val pw = PrintWriter(System.out)

fun main(args : Array<String>) {
    func()
    pw.flush()
}

fun cal(array: MutableList<Int>, num: Int): MutableList<Int> {
    val index = array.indexOfFirst{it == num}
    if (index == -1) {
        array.add(num)
        return array
    } else {
        return array.slice(0..index-1).toMutableList()
    }
} 

fun func() {
    val nk = listOfInt()
    val n = nk[0]
    val k = nk[1]
    val a = listOfInt()

    var state: MutableList<Int> = mutableListOf<Int>()
    var patterns: MutableList<MutableList<Int>> = mutableListOf<MutableList<Int>>()

    for (i in 0..k-1) {
        for (j in 0..n-1) {
            state = cal(state, a[j])
        }

        if (state.count() == 0) {
            break
        }

        var pattern = mutableListOf<Int>()
        pattern.addAll(state)
        patterns.add(pattern)
    }

    if (patterns.count() == 0) {
        println("")
        return
    }

    if (k % (patterns.count() + 1) == 0) {
        println("")
        return
    }

    val index = k % (patterns.count() + 1) - 1
    val pattern = patterns[index]
    var answer = ""
    for (num in pattern) {
        answer += "$num "
    }
    println(answer)
}

fun next() = readLine()!!
fun nextInt() = next().toInt()
fun listOfString() = next().split(" ")
fun listOfInt() = listOfString().map { it.toInt() }

fun println(value : Any) {
    pw.println(value)
}