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;

typedef long long LL;
#define N 220000

LL n,m,k,a[N],vis[N],q[N],f[N][62],lst[N],g[N][62];

int main(){
	srand((unsigned long long)new char+time(NULL));
	scanf("%lld%lld",&n,&m);
	for (int i=1;i<=n;++i) scanf("%lld",a+i);
	for (int i=n;i;--i){
		f[i][0]=lst[a[i]]; g[i][0]=0;
		lst[a[i]]=i;
	}
	for (int i=n;i;--i)
		if (!f[i][0]){f[i][0]=lst[a[i]]; g[i][0]=1;}
	for (int i=1;i<=n;++i)
		if (f[i][0]<n) ++f[i][0];
		else{f[i][0]=1; ++g[i][0];}
	for (int j=1;j<=60;++j){
		for (int i=1;i<=n;++i){
			f[i][j]=f[f[i][j-1]][j-1];
			g[i][j]=g[i][j-1]+g[f[i][j-1]][j-1];
		}
	}
	LL x=1,y=1;
	for (int k=60;~k;--k)
		if (y+g[x][k]<=m){
			y+=g[x][k];
			x=f[x][k];
		}
	int xb=0;
	for (int i=x;i<=n;++i){
		if (!vis[a[i]]){vis[a[i]]=++xb; q[xb]=a[i];}
		else{
			for (;xb>vis[a[i]];--xb){vis[q[xb]]=0; q[xb]=0;}
			vis[q[xb]]=0; q[xb]=0; --xb;
		}
	}
	for (int i=1;i<=xb;++i) printf("%lld ",q[i]);
	puts("");
	
	return 0;
}
			