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.

Examples

Input

3 2
1 2 3


Output

2 3


Input

5 10
1 2 3 2 3


Output

3


Input

6 1000000000000
1 1 2 2 3 3


Output




Input

11 97
3 1 4 1 5 9 2 6 5 3 5


Output

9 2 6
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
const int MAXN = 200005;

int n; lint k;
int a[2 * MAXN];
int mp[2 * MAXN];
lint nxt[60][MAXN];

int main(){
	scanf("%d %lld",&n,&k);
	for(int i=0; i<n; i++) scanf("%d",&a[i]), a[i + n] = a[i];
	for(int i=2*n-1; i>=0; i--){
		if(i < n) nxt[0][i] = mp[a[i]] - i + 1;
		mp[a[i]] = i;
	}
	for(int i=1; i<60; i++){
		for(int j=0; j<n; j++){
			lint sum = nxt[i - 1][j];
			sum += nxt[i - 1][(j + sum) % n];
			sum = min(sum, (lint)1e18);
			nxt[i][j] = sum;
		}
	}
	lint pos = 0;
	for(int i=59; i>=0; i--){
		if(pos + nxt[i][pos % n] <= n * (k - 2)){
			pos += nxt[i][pos % n];
		}
	}
	while(pos < n * k){
		while(pos + nxt[0][pos % n] <= n * k){
			pos += nxt[0][pos % n];
		}
		if(pos == n * k) break;
		printf("%d ", a[pos % n]);
		pos++;
	}
}
