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



Sample input:
3 2
1 2 3


Sample output:
2 3

Submission status: Runtime Error

Solution code:
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
#include<map>
#include<set>
#include<string>
#include<queue>
#include<stack>
using namespace std;
#define MOD 1000000007
#define INF (1<<29)
#define LINF (1LL<<60)
#define EPS (1e-10)
typedef long long Int;
typedef pair<Int, Int> P;


int last[216000];
int bef[216000];
int nxt[216000];
Int n, k, a[216000];
int come[216000];
bool exist[216000];
int main(){
    cin >> n >> k;
    fill(last, last+216000, -1);
    for(int i = 0;i < n;i++){
        cin >> a[i];
        bef[i] = last[a[i]];
        last[a[i]] = i;
    }
    for(int i = 0;i < n;i++){
        if(bef[i] == -1){
            bef[i] = last[a[i]];
        }
        nxt[bef[i]] = i;
    }
    int now = 0;
    int tm = 0;
    do{
        int nxtt = nxt[now];
        tm += nxtt - now;
        if(nxtt <= now)tm += n;
        tm++;
        now = nxtt+1;
        now %= n;
        come[now] = tm;
    }while(now != 0);
    int rem = n * k % come[0];
    while(true){
        int nxtt = nxt[now];
        tm = nxtt - now;
        if(nxtt <= now)tm += n;
        if(rem - tm > 0)rem -= tm;
        else break;
        rem--;
        now = nxtt + 1;
        now %= n;
    }
    vector<int> vec;
    for(int i = 0;i < rem;i++){
        if(exist[a[now]]){
            while(exist[a[now]]){
                exist[vec.back()] = false;
                vec.pop_back();
            }
        }
        else{
            exist[a[now]] = true;
            vec.push_back(a[now]);
        }
        now++;now %= n;
    }
    for(int v:vec)cout << v << " ";
    cout << endl;
    return 0;
}