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;
#define int long long

signed main(){
	int N, K, i, j;
	scanf("%lld%lld", &N, &K);
	vector<int> A(N);
	for(i = 0; i < N; i++){
		scanf("%lld", &A[i]);
	}
	vector<int> AA(2 * N);
	for(i = 0; i < N; i++){
		AA[i] = A[i];
		AA[N + i] = A[i];
	}
	vector<int> next(2 * N), table(200001, 2 * N);
	for(i = 2 * N - 1; i >= 0; i--){
		next[i] = table[AA[i]];
		table[AA[i]] = i;
	}
	int f = 0;
	for(i = 0, j = 0; j < K; ){
//		printf("(i, j) = (%lld, %lld)\n", i, j);
		if(i == 0){
			if(f == 1){
				j = K - K % j;
				if(j == K){
					printf("\n");
					return 0;
				}
			}
			f = 1;
		}
		int nexti = next[i];
		if(nexti < N){
			i = nexti;
		}
		else{
			if(j == K - 1){
				printf("%lld ", AA[i]);
				if(i == N - 1){
					printf("\n");
					return 0;
				}
			}
			else{
				i = nexti % N;
				j++;
			}
		}
		if(i == N - 1){
			i = 0;
			j++;
		}
		else{
			i++;
		}
	}
}