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>
#define last last2

using namespace std;

typedef long long ll;

int f[200005][60];
ll g[200005][60];

int num[400005],last[200005];

void pre(int n) {
  for(int i=0;i<n;i++) num[n+i]=num[i];
  for(int i=2*n-1;i>=0;i--) {
  	if (i<n) {
  		f[i][0]=(last[num[i]]+1)%n;
  		g[i][0]=last[num[i]]-i+1;
	  }
	last[num[i]]=i;
  }
  for(int i=1;i<60;i++)
    for(int j=0;j<n;j++) {
    	f[j][i]=f[f[j][i-1]][i-1];
    	g[j][i]=min(g[j][i-1]+g[f[j][i-1]][i-1],(ll)1e18);
	}
}

int query(ll k) {
  int x=0;
  for(int i=59;i>=0;i--)
    if (g[x][i]<=k) {
    	k-=g[x][i];
    	x=f[x][i];
	}
  return k;
}

int st[200005];
bool vis[200005];

int main() {
  int n;
  ll k;
  scanf("%d%lld",&n,&k);
  for(int i=0;i<n;i++) scanf("%d",&num[i]);
  pre(n);
  int d=query(n*k),top=0;
  for(int i=n-d;i<n;i++) {
  	int x=num[i];
    if (vis[x]) {
    	while (vis[x]) {
    		vis[st[top]]=0;
    		top--;
		}
	}
	else {
		vis[x]=1;
		st[++top]=x;
	}
  }
  for(int i=1;i<=top;i++) printf("%d ",st[i]);
  printf("\n");
  return 0;
}