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;
typedef bool boolean;

#define ll long long

const int N = 2e5 + 5;

int n;
ll K;
int a[N], h[N];
int fa[N], c[N];
boolean vis[N];

int main() {
	scanf("%d%lld", &n, &K);
	for (int i = 0; i < n; i++) {
		scanf("%d", a + i);
	}
	for (int i = n - 1; ~i; i--)
		h[a[i]] = i + n;
	for (int i = n - 1; ~i; i--) {
		int suf = h[a[i]];
		fa[i] = (suf + 1) % n;
		c[i] = (suf + 1) / n;
		h[a[i]] = i;
	}
	int p = 0, q;
	vector<int> stk;
	do {
		vis[p] = true;
		stk.push_back(p);
		p = fa[p];
	} while (!vis[p]);
	int sumcost = 0;
	do {
		q = stk.back();
		stk.pop_back();
		sumcost += c[q];
	} while (q ^ p);
	stk.clear();
	int x = 0;
	while (K - c[x] >= 1 && (x ^ p))
		K -= c[x], x = fa[x];
	if (x == p)
		K = (K - 1) % sumcost + 1;
	while (K - c[x] >= 1)
		K -= c[x], x = fa[x];
	memset(vis, false, sizeof(vis));
	for (int i = x; i < n + (K - 1) * n; i++) {
		int z = a[i % n];
		if (!vis[z]) {
			stk.push_back(z);
			vis[z] = true;
		} else {
			int y = 0;
			do {
				y = stk.back();
				stk.pop_back();
				vis[y] = false;
			} while (y ^ z);
		}
	}
	for (auto x : stk) {
		printf("%d ", x);
	}
	return 0;
}
