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
//by yjz
#include<bits/stdc++.h>
#define FF first
#define SS second
#define MP make_pair
#define PB push_back
typedef long long ll;
using namespace std;
const int maxn = 200111*2;
const ll inf = 1e18;
int n;
ll K;
int a[maxn];
int len[maxn];
int lst[maxn];
ll go[60][maxn], glen[60][maxn];
vector<int> ans;
map<int,int> mp;
void add(int x)
{
	if (mp[x]==0)
	{
		ans.PB(x);
		mp[x]++;
	}
	else
	{
		while (mp[x]>0)
		{
			mp[ans.back()]--;
			ans.pop_back();
		}
	}
}
int main()
{
	cin>>n>>K;
	for (int i=0; i<n; i++) scanf("%d", &a[i]), a[n+i] = a[i];
	int r = n+n;
	for (int i=n+n-1; i>=0; i--)
	{
		if (lst[a[i]])
		{
			len[i] = lst[a[i]]-i+1;
		}
		lst[a[i]] = i;
	}
	for (int i=0; i<n; i++) cerr<<len[i]<<" "; cerr<<endl;
	for (int i=0; i<n; i++)
	{
		go[0][i] = (i+len[i])%n;
		glen[0][i] = len[i];
	}
	for (int i=1; i<60; i++)
	{
		for (int j=0; j<n; j++)
		{
			go[i][j] = go[i-1][go[i-1][j]];
			glen[i][j] = min(inf, glen[i-1][j]+glen[i-1][go[i-1][j]]);
		}
	}
	K = 1ll*K*n;
	int cur = 0;
	for (int i=59; i>=0; i--)
	{
		if (glen[i][cur]<=K)
		{
			K -= glen[i][cur];
			cur = go[i][cur];
		}
	}
	for (int i=0; i<K; i++)
	{
		add(a[(cur+i)%n]);
	}
	for (auto x : ans) printf("%d ", x);
	return 0;
}