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;
typedef vector<int> vi;
typedef vector<vi> vvi;
const int MN = 200200;
const int MM = MN*2;
int w[MM],x[MM];
vvi nx;
int bs[MM];
int main() {
	ios::sync_with_stdio(0);
	ll n,k;
	cin >> n >> k;
	for(int i=0;i<n;i++) {
		cin >> w[i];
		w[i+n] = w[i];
	}
	nx.assign(MN,vi());
	for(int i=0;i<n*2;i++) {
		nx[w[i]].push_back(i);
	}
	for(int i=0;i<n;i++) {
		int val = w[i];
		int id = *upper_bound(nx[val].begin(),nx[val].end(),i);
		id++;
		bs[i] = id/n;
		id %= n;
		x[i] = id;
	}
	ll cl = bs[0];
	ll pt = x[0];
	while(pt != 0) {
		cl += bs[pt];
		pt = x[pt];
	}
	k %= cl;
	bitset<MM> bb;
	vi res;
	while(k) {
		if(bs[pt] >= k) {
			break;
		}
		k -= bs[pt];
		pt = x[pt];
	}
	while(k) {
		int val = w[pt];
		if(bb[val]) {
			while(bb[val]) {
				bb.reset(res.back());
				res.pop_back();
			}
		} else {
			bb.set(val);
			res.push_back(val);
		}
		pt++;
		if(pt >= n) {pt -= n;k--;}
	}
	for(int i=0;i<res.size();i++) {
		if(i > 0) {cout << " ";}
		cout << res[i];
	}
	cout << '\n';
}