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 rep(i,n) for(int i = 0; i < n; i++)
const int mx = 200005;
int n, a[mx], nx[mx], s = 1, t, nw[mx], f[mx];
vector<int> ans;
long long k;
int main(){
	scanf("%d%lld", &n, &k);
	rep(i,mx) f[i] = nw[i] = -1;
	rep(i,n){
		scanf("%d", a+i);
		a[i]--;
		if(nw[a[i]] != -1) nx[nw[a[i]]] = i;
		else f[a[i]] = i;
		nx[i] = f[a[i]];
		nw[a[i]] = i;
	}
	
	while(t != n){
		if(nx[t] <= t) s++;
		t = nx[t] + 1;
	}
	k %= s;
	if(k == 0) return 0*puts("");
	s = 0;t = 0;
	while(true){
		if(nx[t] <= t) s++;
		if(s == k) break;
		t = nx[t] + 1;
	}
	while(t<n){
		if(nx[t] <= t) ans.push_back(a[t]);
		else t = nx[t];
		t++;
	}
	rep(i,ans.size()) printf("%d%s", ans[i]+1, i+1==ans.size() ? "\n" : " ");
}