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 cs const
#define pb push_back
using namespace std;
typedef long long ll;
cs int N = 2e5 + 50;
int n, a[N], lp[N]; ll k;
int main(){
	#ifdef FSYolanda
	freopen("1.in","r",stdin);
	#endif
	scanf("%d%lld",&n,&k);
	for(int i=1; i<=n; i++) 
	scanf("%d",&a[i]);
	static int la[N];
	for(int i=1; i<=n; i++)
	if(!la[a[i]]) la[a[i]] = n+i;
	for(int i=n; i>=1; i--)
	lp[i]=la[a[i]], la[a[i]]=i;
	static int r[N];
	for(int i=1,x=1,c=1;;i++){
		if(i>1 && x==1){
			k = k % c ? k % c : c;
			break;
		} r[x] = c;
		if(lp[x] > n) ++c;
		x = lp[x] % n + 1;
	}
	for(int i=n; i>=1; i--) if(r[i] == k){
		static bool ex[N];
		memset(ex, 0 , sizeof(ex));
		static int stk[N]; int top = 0;
		for(int j = i; j <= n; j++){
			if(ex[a[j]]){
				while(stk[top] != a[j]) 
				ex[stk[top]] = false, --top;
				ex[a[j]] = false, --top;
			} else stk[++top] = a[j], ex[a[j]] = true;
		} for(int j = 1; j <= top; j++) cout << stk[j] << " ";
		return 0;
	}
	return 0;
}