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;
						
#define fast_cin() ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0)
#define endl '\n'
#define int long long

const int N = 4e5 + 5, LG = 60;
const int inf = 1e18;

int jumpDist[N][LG];
int a[N], nxtOcc[N];
				
int32_t main() {
	fast_cin();  
	int n, k; cin >> n >> k;
	for (int i = 0; i < n; ++i) {
		cin >> a[i];
		a[i + n] = a[i];
	}
	for (int i = 2 * n - 1; i >= 0; --i) {
		if (i < n) {
			jumpDist[i][0] = (nxtOcc[a[i]] - i) + 1;
		}
		nxtOcc[a[i]] = i;
	}
	// binary lifting
	for (int j = 1;  j < LG; ++j) {
		for (int i = 0; i < n; ++i) {
			jumpDist[i][j] = min(inf, jumpDist[i][j - 1] + jumpDist[(i + jumpDist[i][j - 1]) % n][j - 1]);
		}
	}
	int curloc = 0;
	for (int j = LG - 1; j >= 0; --j) {
		if (curloc + jumpDist[curloc % n][j] <= n * k) {
			curloc += jumpDist[curloc % n][j];
		}
	}
	vector<int> ans;
	while (curloc < n * k) {
		if (curloc + jumpDist[curloc % n][0] <= n * k) {
			curloc += jumpDist[curloc % n][0];
		} else {
			ans.push_back(a[curloc % n]);
			++curloc;
		}
	}
	for (int &i : ans) {
		cout << i << " ";
	}
	cout << endl;
	return 0;
}