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;

int N, A[400009], nx[200009], c[200009], P[200009];
long long K, L, fi[200009], a, b;

void putans(int x) {
	vector<int> S;
	vector<bool> chk(200009, 0);
	for(int i=x; i<N; i++) {
		if(chk[A[i]]) {
			while(chk[A[i]]) {
				chk[S.back()] = 0;
				S.pop_back();
			}
		}
		else {
			chk[A[i]] = 1;
			S.push_back(A[i]);
		}
	}
	for(auto& it: S) printf("%d ", it);
	exit(0);
}

void go(int i, long long d) {
	if(fi[i] != -1) {
		a = fi[i];
		b = d - fi[i];
		return;
	}
	fi[i] = d;
	go(nx[i], d + c[i]);
}

void Do(int i, long long d) {
	if(d + c[i] <= L) Do(nx[i], d + c[i]);
	else putans(i);
}

int main() {
	scanf("%d%lld",&N,&K);
	L = K*N;
	for(int i=0; i<N; i++) {
		scanf("%d",&A[i]);
		A[i+N] = A[i];
		fi[i] = -1;
	}
	for(int i=2*N-1; i>=0; i--) {
		if(i < N) nx[i] = (P[A[i]] + 1) % N, c[i] = P[A[i]] - i + 1;
		P[A[i]] = i;
	}
	go(0, 0);
	if(L <= a) Do(0, 0);
	else {
		L -= a;
		L %= b;
		if(L == 0) return 0;
		Do(0, 0);
	}
	return 0;
}