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>
typedef long long LL;
const int M = 200007;

int n; LL m;
int fir[M], las[M], nxt[M];
int jp[M], stp[M], ans[M];
int a[M];

LL getloop() {
	int x = 1;
	LL res = 0;
	do {
		res += stp[x];
		x = jp[x];
	} while(x != 1);
	return res;
}

int main() {

	std::ios::sync_with_stdio(false);
	std::cin >> n >> m;
	LL s = n * m;

	for (int i = 1; i <= n; ++i) std::cin >> a[i];
	for (int i = 1; i <= n; ++i) if (!fir[a[i]]) fir[a[i]] = i;
	for (int i = n; i >= 1; --i) {
		if (!las[a[i]]) {
			nxt[i] = fir[a[i]];
		}
		else nxt[i] = las[a[i]];
		las[a[i]] = i;
	}
	for (int i = 1; i <= n; ++i) {
		jp[i] = nxt[i] == n ? 1 : nxt[i] + 1;
		stp[i] = nxt[i] > i ? nxt[i] - i + 1 : nxt[i] + n - i + 1;
	}

	LL d = getloop();
	s = s % d;

	int x = 1;
	while (s >= stp[x]) {
		s -= stp[x];
		x = jp[x];
	}
	if (s != 0) {
		memset(las, 0, sizeof las);
		int tot = 0;
		while (s--) {
			if (!las[a[x]]) {
				ans[++tot] = a[x];
				las[a[x]] = tot;
			}
			else {
				for (int tmp = las[a[x]] - 1; tot > tmp; --tot) 
					las[ans[tot]] = 0;
			}
			x = x == n ? 1 : x + 1;
		}
		assert(tot != 0);
		for (int i = 1; i <= tot; ++i) {
			std::cout << ans[i] << (i == tot ? "" : " ");
		}
		std::cout << std::endl;
	}
	
	return 0;
}
