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<iostream>
#include<cstdio>
#include<fstream>
	using namespace std;
	int a[500005],g[200005],ans[200005];
	long long f[200005][70];
int main()
{
	int n=0;
	long long k=0;
	scanf("%d%lld",&n,&k);
	for(int i=1;i<=n;i++)
		scanf("%d",&a[i]),a[n+i]=a[i];
	for(int i=1;i<=n+n;i++)
	{
		if(0<g[a[i]]&&g[a[i]]<=n)
			f[g[a[i]]][0]=i-g[a[i]]+1;
		g[a[i]]=i;
	}
	for(int j=1;j<=65;j++)
		for(int i=1;i<=n;i++)
		{
			int s=((i+f[i][j-1])%n==0)?n:(i+f[i][j-1])%n;
			if(f[i][j-1]==-1||f[s][j-1]==-1) f[i][j]=-1;
			else f[i][j]=f[i][j-1]+f[s][j-1];
			if(f[i][j]<0) f[i][j]=-1;
		}
	long long c=1;
	for(int i=65;i>=0;i--)
	{
		int s=(c%n==0)?n:c%n;
		long long h=c+f[s][i];
		if(h<0||h>n*k) h=-1;
		if(f[s][i]!=-1&&h!=-1) c+=f[s][i];
	}
	int cnt=0; c=n*k-c+1;
	if(c>n) c=0;
	for(int i=1;i<=n;i++) g[a[i]]=0;
	for(int i=n-c+1;i<=n;i++)
		if(g[a[i]])
			while(g[a[i]])
				g[ans[cnt--]]=0;
		else g[a[i]]=1,ans[++cnt]=a[i];
	for(int i=1;i<=cnt;i++) printf("%d ",ans[i]);
	return 0;
}