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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define ll long long

ll n,k;
int arr[200005];
vector<int> pos[200005];
int nxt[200005];

vector<int> fin;
bool used[200005];

int norm(int i){
	while (i<=0) i+=n;
}

int main(){
	cin>>n>>k;	
	
	for (int x=0;x<n;x++){
		cin>>arr[x];
		pos[arr[x]].push_back(x);
	}
	
	for (int x=0;x<200005;x++){
		for (int y=0;y<pos[x].size();y++){
			nxt[pos[x][y]]=pos[x][(y+1)%pos[x].size()];
		}
	}
	
	int period=1;
	int curr=0;
	
	while (curr!=n){
		if (nxt[curr]<=curr) period++;
		curr=nxt[curr];
		
		curr++;
	}
	
	k%=period;
	
	if (k==0) return 0;
	
	curr=0;
	while (k>1){
		if (nxt[curr]<=curr) k--;
		curr=nxt[curr]+1;
	}
	
	for (int x=curr;x<n;x++){
		if (used[arr[x]]){
			while (used[arr[x]]){
				used[fin.back()]=false;
				fin.pop_back();
			}
		}
		else{
			fin.push_back(arr[x]);
			used[arr[x]]=true;
		}
	}
	
	for (auto &it:fin) cout<<it<<" ";
}