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>
#include <climits>

typedef long long LL;
const LL Inf = LLONG_MAX / 3;
const int MN = 400005;

int N, A[MN], buk[MN];
LL K, L, Dis[MN][61]; int Bit;
int stk[MN], tp;

int main() {
	scanf("%d%lld", &N, &K), L = N * K;
	for (int i = 1; i <= N; ++i) scanf("%d", &A[i]), A[N + i] = A[i];
	for (int i = N + N; i >= 1; --i) {
		if (i <= N) Dis[i][0] = buk[A[i]] - i + 1;
		buk[A[i]] = i;
	}
	for (int j = 0; j < 59; ++j) {
		LL Mn = Inf;
		for (int i = 1; i <= N; ++i)
			Dis[i][j + 1] = std::min(Inf, Dis[i][j] + Dis[(i + Dis[i][j] - 1) % N + 1][j]),
			Mn = std::min(Mn, Dis[i][j]);
		Bit = j + 1;
		if (Mn > L) break;
	}
	LL S = 1;
	for (int j = Bit; ~j; --j)
		if (S + Dis[(S - 1) % N + 1][j] <= L)
			S += Dis[(S - 1) % N + 1][j];
	for (int i = 1; i <= N; ++i) buk[A[i]] = 0;
	int p = N + N - L + S;
	for (int i = p; i <= N + N; ++i) {
		if (!buk[A[i]]) stk[++tp] = A[i], buk[A[i]] = 1;
		else {
			while (stk[tp] != A[i]) buk[stk[tp--]] = 0;
			buk[stk[tp--]] = 0;
		}
	}
	for (int i = 1; i <= tp; ++i) printf("%d%c", stk[i], " \n"[i == tp]);
	return 0;
}