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;
const int N = 200005;
int n;
long long k;
int a[N], lst[N], nxt[N];
long long used[N];
int main() {
	scanf("%d%lld", &n, &k);
	for (int i = 1; i <= n; i++) {
		scanf("%d", &a[i]);
	}
	for (int i = 1; i <= 200000; i++) lst[i] = n + 1;
	for (int i = n; i >= 1; i--) {
		nxt[i] = lst[a[i]];
		lst[a[i]] = i;
	}
	long long cnt = 1, id = 1;
	while (true) {
		if (!used[id]) {
			used[id] = cnt;
		} else {
			long long x1 = used[id], x2 = cnt;
			long long want = (k - x1) % (x2 - x1) + x1;
			int gay = 0;
			for (int i = 1; i <= 200000; i++) if (used[i] == want) {gay = i; break;}
			cnt = k;
			id = gay;
			break;
		}
		if (nxt[id] == n + 1) {
			if (cnt == k) {
				break;
			}
			cnt++;
			id = lst[a[id]];
		} else {
			id = nxt[id];
		}
		id++;
		if (id == n + 1) {
			if (cnt == k) {
				return 0;
			}
			cnt++;
			id = 1;
		}
	}
	while (true) {
		if (id > n) break;
		if (nxt[id] <= n) {
			id = nxt[id] + 1;
		} else {
			printf("%d ", a[id]);
			id++;
		}
	}
	return 0;
}