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 long long ll;
#define DBG(v) cerr << #v << " = " << (v) << endl;

const int MxN = (int) 2e5 + 9;
int nxt[MxN + 9];
int dist[MxN + 9];

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr), cout.tie(nullptr);

	int n;
	ll K;
	cin >> n >> K;
	vector<int> a(n);
	for (int &x : a)
		cin >> x;

	vector<int> dp(n + 1, 0);
	map<int, int> mp;
	for (int i = n - 1; i >= 0; --i) {
		if (mp.count(a[i]))
			dp[i] = dp[mp.at(a[i]) + 1];
		else
			dp[i] = a[i];
		mp[a[i]] = i;
	}

	nxt[0] = dp[0];
	for (int x = 1; x <= MxN; ++x) {
		if (mp.count(x))
			nxt[x] = dp[mp.at(x) + 1];
	}

	memset(dist, -1, sizeof dist);
	int cLen;
	for (int d = 0, x = 0;; x = nxt[x], ++d) {
		if (dist[x] == -1)
			dist[x] = d;
		else {
			cLen = d - dist[x];
			break;
		}
	}

	K -= 4 * MxN;
	if (K > 0)
		K %= cLen;
	K += 4 * MxN;

	int x = 0;
	for (; K > 1; K--)
		x = nxt[x];

	vector<int> v;
	set<int> s;
	if (x) {
		v.push_back(x);
		s.insert(x);
	}

	for (const int x : a) {
		if (!s.count(x)) {
			s.insert(x);
			v.push_back(x);
		} else
			while (s.count(x)) {
				assert(!v.empty());
				s.erase(v.back());
				v.pop_back();
			}
	}
	for (int x : v)

		cout << x << ' ';
	return 0;
}
