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> 
long long K;
int k,n,tot,WZ;
int a[234234],fir[234234],go[234234],wz[234234];

int main()
{
  int i;
  scanf("%d%lld",&n,&K);
  for(i=1;i<=n;i++) 
    {
	 scanf("%d",&a[i]);
	 if(!fir[a[i]]) fir[a[i]]=i;}
  for(i=n;i>=1;i--)
    {
	  if(!wz[a[i]]) go[i]=fir[a[i]];
	  else go[i]=wz[a[i]];
	  wz[a[i]]=i;
	}
  tot=1,WZ=1;	
  while(1)
  {
    
    if(go[WZ]<=WZ) tot++;
    WZ=go[WZ]+1; 
    if(WZ==n+1) break;
  }
  k=K%tot;
  if(!k) return 0;
  WZ=1;
  while(1)
    {
    	if(k==1) break;
      	if(go[WZ]<=WZ) k--;
    WZ=go[WZ]%n+1; 
    }
  while(WZ<=n)
  {
    if(go[WZ]>WZ) WZ=go[WZ];
    else printf("%d ",a[WZ]);
    WZ++;
  }
}