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: Accepted)

#[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], param[1]);
    let arr = read_vector::<u64>();
    if n == 1 && k == 1 {
        println!("{}", arr[0]);
        return;
    }
    let mut positions = HashMap::<u64, Vec<u64>>::new();
    for i in 0..arr.len() {
        if positions.contains_key(&arr[i]) {
            positions.get_mut(&arr[i]).unwrap().push(i as u64);
        } else {
            positions.insert(arr[i], vec![i as u64]);
        }
    }
    let mut dp = vec![vec![n * k + 1; arr.len()]; ((n * k) as f64).log2() as usize];
    for (_, indices) in positions.into_iter() {
        for i in 0..indices.len() {
            if i < indices.len() - 1 {
                dp[0][indices[i] as usize] = indices[i + 1] - indices[i] + 1;
            } else {
                dp[0][indices[i] as usize] = indices[0] + n - indices[i] + 1;
            }
        }
    }
    for i in 1..dp.len() {
        for j in 0..arr.len() {
            dp[i][j] = min(dp[i - 1][j] + dp[i - 1][((j as u64 + dp[i - 1][j]) % n) as usize], dp[i][j]);
        }
    }
    let mut index = 0;
    let mut crt = 0;
    while index < n * (k - 1) {
        for i in (0..dp.len()).rev() {
            if index + dp[i][crt] > n * k {
                continue;
            }
            index += dp[i][crt];
            crt = (index % n) as usize;
        }
    }
    if index == n * k {
        println!("");
        return;
    }
    for elem in solve(&arr, crt).into_iter() {
        print!("{} ", elem);
    }
    println!("");
}

fn solve(arr: &[u64], init: usize) -> Vec<u64> {
    let mut ans = vec![];
    let mut nums = HashMap::new();
    for i in init..arr.len() {
        if nums.contains_key(&arr[i]) {
            let j = *nums.get(&arr[i]).unwrap();
            for k in (j..ans.len()).rev() {
                nums.remove(&ans[k]);
                ans.pop().unwrap();
            }
        } else {
            nums.insert(arr[i], ans.len());
            ans.push(arr[i]);
        }
    }
    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();
}