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: Time Limit Exceeded)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String {
            bytes
                .by_ref()
                .map(|r| r.unwrap() as char)
                .skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{min, max};
use std::collections::{HashMap, HashSet};

fn main() {
    input!{
        n: usize,
        k: usize,
        v: [usize; n]
    }
    let mut dels: HashSet<usize> = HashSet::new();
    let mut w = vec![];
    let mut map: HashMap<usize, usize> = HashMap::new();
    let mut rep = false;
    for &x in &v {
        if map.contains_key(&x) {
            loop {
                let y = w.pop().unwrap();
                *map.get_mut(&y).unwrap() -= 1;
                if map.get(&y) == Some(&0) {
                    map.remove(&y);
                    dels.insert(y);
                }
                if y == x {
                    break;
                }
            }
        } else {
            if dels.contains(&x) {
                rep = true;
            }
            map.insert(x, 1);
            w.push(x);
        }
    }
    let mut c;
    if rep {
        c = 1;
        let mut w2 = w.clone();
        while w2.len() > 0 {
            update(&mut w2, &v);
            c += 1;
        }
    } else {
        c = w.len() + 1;
    }
    let k = k % c;
    if k > 0 {
        if !rep {
            print!("{}", w[k - 1]);
            for i in k..w.len() {
                print!(" {}", w[i]);
            }
        } else {
            for i in 1..k {
                update(&mut w, &v);
            }
            print!("{}", w[0]);
            for i in 1..w.len() {
                print!(" {}", w[i]);
            }
        }
    }
    println!("");
}

fn update(w: &mut Vec<usize>, v: &Vec<usize>) {
    let mut map: HashMap<usize, usize> = HashMap::new();
    for &x in w.iter() {
        map.insert(x, 1);
    }
    for &x in v {
        if map.contains_key(&x) {
            loop {
                let y = w.pop().unwrap();
                *map.get_mut(&y).unwrap() -= 1;
                if y == x {
                    map.remove(&y);
                    break;
                }
                if map.get(&y) == Some(&0) {
                    map.remove(&y);
                }
            }
        } else {
            map.insert(x, 1);
            w.push(x);
        }
    }
}