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<cstdio>
#include<algorithm>
using namespace std;
int n;
int w[401000], P[401000];
long long K, Nxt[201000][41];
int U[401000], C[401000];
int main() {
	int i, j;
	scanf("%d%lld", &n, &K);
	for (i = 1; i <= n; i++) {
		scanf("%d", &w[i]);
		w[n + i] = w[i];
	}
	for (i = n + n; i >= 1; i--) {
		if (i <= n) {
			Nxt[i - 1][0] = P[w[i]] - (i - 1);
		}
		P[w[i]] = i;
	}
	for (i = 0; i < 40; i++) {
		for (j = 0; j < n; j++) {
			Nxt[j][i+1] = Nxt[j][i] + Nxt[(j+Nxt[j][i])%n][i];
		}
	}
	long long s = 0;
	int cur = 0;
	for (i = 40; i >= 0; i--) {
		while (s + Nxt[cur][i] <= n*K) {
			s += Nxt[cur][i];
			cur = s % n;
		}
	}
	if (s == n * K) {
		return 0;
	}
	int cnt = 0;
	for (long long ii = s; ii < n * K; ii++) {
		int t = w[ii % n + 1];
		if (C[t]) {
			while (C[t]) {
				cnt--;
				C[U[cnt]]--;
			}
		}
		else {
			U[cnt++] = t;
			C[t]++;
		}
	}
	for (i = 0; i < cnt; i++)printf("%d ", U[i]);
}