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 lint long long

const int N = 4e5 + 10;

int a[N];
int nxt[N], pos[N];
int vis[N];

int main (void) {
	int n; lint k;
	scanf("%d%lld", &n, &k);
	for (int i = 1; i <= n; i++) {
		scanf("%d", a + i);
	}
	if (n == 1) {
		if (k & 1) printf("%d\n", a[1]);
		else puts("");
		return 0;
	}

	memcpy(a + n + 1, a + 1, sizeof(int) * n);
	for (int i = 1; i <= 2 * n; i++) {
		if (pos[a[i]]) nxt[pos[a[i]]] = i;
		pos[a[i]] = i;
	}
	for (int i = 1; i <= n; i++) {
		if (nxt[i] > n) nxt[i] -= n;
	}
	int loop = 1, cur = 0;
	pos[1] = 0;
	while (cur != n) {
		cur ++;
		if (cur >= nxt[cur]) {
			cur = nxt[cur];
			pos[++ loop] = cur;
		} else {
			cur = nxt[cur];
		}
	}
	k %= loop;
	if (k != 0) {
		vector<int> v;
		for (int i = pos[k] + 1; i <= n; i++) {
			if (!vis[a[i]]) {
				v.push_back(a[i]);
				vis[a[i]] = 1;
			} else {
				while (v.back() != a[i]) {
					vis[v.back()] = 0;
					v.pop_back();
				}
				vis[v.back()] = 0;
				v.pop_back();
			}
		}
		for (int i = 0, sz = v.size(); i < sz; i++) {
			printf("%d%c", v[i], "\n "[i != sz - 1]);
		}
	}
}