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 Rust (1.15.1) (judge verdict: Wrong Answer)

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::prelude::BufRead;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufReader, BufWriter, Write};
#[allow(unused_imports)]
use std::mem::swap;
#[allow(unused_imports)]
use std::str::FromStr;


fn main() {
    let param = read_vector::<u64>();
    let (n, k) = (param[0] as usize, param[1]);
    let arr = read_vector::<usize>();
    let mut period = vec![0];
    let mut first = HashMap::new();
    for i in 0..n {
        if !first.contains_key(&arr[i]) {
            first.insert(arr[i], i);
        }
    }
    let mut init = 0;
    loop {
        if let Some(first_num) = operate(&arr, init) {
            init = *first.get(&first_num).unwrap() + 1;
            period.push(init);
        } else {
            break;
        }
    }
    let start = ((k % period.len() as u64) as usize + period.len() - 1) % period.len();
    let ans = solve(&arr, start);
    for i in 0..ans.len() {
        if i < ans.len() - 1 {
            print!("{} ", ans[i]);
        } else {
            print!("{}", ans[i]);
        }
    }
    println!("");
}

fn operate(arr: &[usize], init: usize) -> Option<usize> {
    if init == arr.len() {
        return None;
    }
    let mut first_num = arr[init];
    let mut index = init + 1;
    while index < arr.len() {
        if arr[index] == first_num {
            if index == arr.len() - 1 {
                return None;
            }
            first_num = arr[index + 1];
            index = index + 2;
        } else {
            index += 1;
        }
    }
    Some(first_num)
}

fn solve(arr: &[usize], init: usize) -> Vec<usize> {
    let mut ans = vec![];
    if init == arr.len() {
        return ans;
    }
    let mut nums = HashMap::new();
    let mut index = 0;
    for i in init..arr.len() {
        if nums.contains_key(&arr[i]) {
            let j = *nums.get(&arr[i]).unwrap();
            nums.remove(&arr[i]);
            if j < index {
                index = j;
            } else {
                ans[index] = arr[i];
                nums.insert(arr[i], index);
                index += 1;
            }
        } else {
            if index == ans.len() {
                ans.push(arr[i]);
            } else {
                ans[index] = arr[i];
            }
            nums.insert(arr[i], index);
            index += 1;
        }
    }
    while ans.len() != index {
        ans.pop().unwrap();
    }
    ans
}

#[allow(dead_code)]
fn read<T>() -> T where T: std::str::FromStr, T::Err: std::fmt::Debug {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    return buf
        .trim()
        .parse()
        .unwrap();
}

#[allow(dead_code)]
fn read_vector<T>() -> Vec<T> where T: std::str::FromStr, T::Err: std::fmt::Debug {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    return buf
        .split_whitespace()
        .map(|s| s.parse().unwrap())
        .collect();
}

#[allow(dead_code)]
fn read_matrix<T>() -> Vec<Vec<T>> where T: std::str::FromStr, T::Err: std::fmt::Debug {
    use std::io::prelude::*;
    let stdin = stdin();
    return stdin
        .lock()
        .lines()
        .map(|line| line
            .unwrap()
            .split_whitespace()
            .map(|s| s.parse().unwrap())
            .collect())
        .collect();
}