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>
#include <set>

using namespace std;

typedef long long ll;

int n;
ll k;
int a[202020];
int f[202020];
int d[202020];

int main() {
	cin >> n >> k;
	for (int i = 1; i <= n; i++) cin >> a[i];
	for (int i = n; i >= 1; i--) {
		f[i] = d[a[i]];
		d[a[i]] = i;
	}
	int p = 1;
	int c = 1;
	while (true) {
		if (f[p] != 0) {
			p = f[p];
		} else {
			p = d[a[p]];
			c++;
		}
		if (p == n) break;
		p++;
	}
	k %= c;
	p = 1;
	c = 1;
	while (c < k) {
		if (f[p] != 0) {
			p = f[p];
		} else {
			p = d[a[p]];
			c++;
		}
		p++;
	}
	vector<int> u;
	set<int> s;
	for (int i = p; i <= n; i++) {
		if (s.count(a[i])) {
			while (s.count(a[i])) {
				s.erase(u.back());
				u.pop_back();
			}
		} else {
			u.push_back(a[i]);
			s.insert(a[i]);
		}
	}
	for (auto x : u) cout << x << " ";
	cout << "\n";
}
