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 <iostream>
#include <vector>

constexpr int ELM = 200200;
constexpr int LG = 60;
constexpr long long INF = 1e18;

int main() {
	int n;
	long long k;
	std::cin >> n >> k;
	const long long MAX = n * k;
	std::vector<int> a(n);
	for (int i = 0; i < n; i++) {
		std::cin >> a[i];
	}
	
	std::vector<std::vector<long long>> next(LG, std::vector<long long>(n));
	std::vector<int> idx(ELM, -1);
	for (int id = 2 * n; id --> 0;) {
		int i = id % n;
		if (id < n) next[0][i] = idx[a[i]] - i + 1;
		idx[a[i]] = id;
	}
	
	for (int i = 1; i < LG; i++) {
		for (int j = 0; j < n; j++) {
			int id = (next[i - 1][j] + j) % n;
			next[i][j] = std::min(INF, next[i - 1][j] + next[i - 1][id]);
		}
	}
	
	long long s = 0;
	for (int i = LG; i --> 0;) {
		int id = s % n;
		if (s + next[i][id] <= MAX) s += next[i][id];
	}
	
	std::vector<int> sec;
	while (s < MAX) {
		int i = s % n;
		if (s + next[0][i] <= MAX) {
			s += next[0][i];
		} else {
			sec.push_back(a[i]);
			s++;
		}
	}
	
	for (auto e : sec) std::cout << e << ' ';

	return 0;
}