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)

//use rand::Rng;
use std::collections::{BTreeMap, BTreeSet};

fn main() {
    //    let mut rng = rand::thread_rng();
    //    loop {
    //        let n = 5;
    //        let a: Vec<u64> = (0..n).map(|_| rng.gen::<u64>() % (n as u64) + 1).collect();
    //
    //        let ans1 = solve(&a, n);
    //        let ans2 = naive(&a, 0, n);
    //        assert_eq!(ans1, ans2, "a={:?} naive={:?} solve={:?}", a, ans2, ans1);
    //    }

    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let n = sc.read();
    let k: usize = sc.read();
    let a: Vec<u64> = sc.vec(n);

    let ans = solve(&a, k * n);
    for (i, a) in ans.into_iter().enumerate() {
        if i > 0 {
            print!(" ");
        }
        print!("{}", a);
    }
    println!();
}

fn solve(a: &Vec<u64>, l: usize) -> Vec<u64> {
    let n = a.len();
    let mut prev = BTreeMap::new();
    let mut jump = vec![vec![0; n]; 50];

    for i in 0..n {
        if prev.contains_key(&a[i]) {
            let x = prev[&a[i]];
            jump[0][x] = i - x;
            prev.insert(a[i], i);
        } else {
            prev.insert(a[i], i);
        }
    }

    for i in 0..n {
        if let Some(x) = prev.remove(&a[i]) {
            jump[0][x] = n + i - x;
        }
    }

    for t in 1..50 {
        for i in 0..n {
            let jump1 = jump[t - 1][i];
            let next = (i + jump1 + 1) % n;
            let jump2 = jump[t - 1][next];
            jump[t][i] = jump1 + 1 + jump2;
        }
    }

    let mut pos = 0;
    for t in (0..50).rev() {
        loop {
            let next = jump[t][pos % n] + pos + 1;
            if next < l {
                pos = next;
            } else {
                break;
            }
        }
    }
    assert!(pos < l);

    naive(&a, pos, l)
}

fn naive(a: &Vec<u64>, pos: usize, l: usize) -> Vec<u64> {
    let n = a.len();
    let mut set = BTreeSet::new();
    let mut ans = vec![];
    for i in pos..l {
        let d = i % n;
        let a = a[d];
        if set.contains(&a) {
            while let Some(p) = ans.pop() {
                set.remove(&p);
                if p == a {
                    break;
                }
            }
            set.remove(&a);
        } else {
            set.insert(a);
            ans.push(a);
        }
    }
    ans
}

pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}