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 LL long long

const int maxN = 2e5 + 10;

int a[maxN + 1], n;
int last[maxN + 1], fir[maxN + 1], nxt[maxN + 1][42];
int stk[maxN + 1], top;
LL m;
bool flag[maxN + 1];

int main()
{
	scanf("%d %lld", &n, &m);
	for(int i = 1; i <= n; i++) scanf("%d", &a[i]);

	for(int i = n; i >= 1; i--)
	{
		if(!last[ a[i] ]) fir[i] = a[i];
		else fir[i] = fir[ last[ a[i] ] + 1 ];
		last[ a[i] ] = i;
	}

	nxt[n + 1][0] = 1;
	for(int i = 1; i <= n; i++) 
		nxt[i][0] = last[ fir[i] ] + 1;
	
	for(int j = 1; j <= 40; j++)
		for(int i = 1; i <= n + 1; i++)
			nxt[i][j] = nxt[ nxt[i][j - 1] ][j - 1];
	
	int x = n + 1;
	for(int i = 40; i >= 0; i--)
		if(m >= (1ll << i)) x = nxt[x][i], m -= (1ll << i);

	top = 0;
	for(int i = x; i <= n; i++)
	{
		int t = a[i];
		if(!flag[t]) stk[++ top] = t, flag[t] = true;
		else
		{
			while(stk[top] != t) flag[ stk[top] ] = false, top --;
			flag[ stk[top] ] = false; top --;
		}
	}

	for(int i = 1; i <= top; i++) printf("%d ", stk[i]);
	puts("");
	return 0;
}
