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;

const ll INF = 2e18;

const int MAXN = 2.1e5;
int N;
ll K;
int A[MAXN];

const int MAXV = 2.1e5;
int nxtOcc[MAXV];

const int L = 60;
ll jumpDist[MAXN][L + 1];

int main() {
	scanf("%d %lld", &N, &K);
	for (int i = 0; i < N; i++) {
		scanf("%d", &A[i]);
	}

	// cyclic
	for (int i = N-1; i >= 0; i--) {
		nxtOcc[A[i]] = i+N;
	}
	for (int i = N-1; i >= 0; i--) {
		jumpDist[i][0] = (nxtOcc[A[i]] - i) + 1;
		nxtOcc[A[i]] = i;
	}

	for (int l = 0; l < L; l++) {
		for (int i = 0; i < N; i++) {
			jumpDist[i][l+1] = min(INF, jumpDist[i][l] + jumpDist[(i + jumpDist[i][l]) % N][l]);
		}
	}

	ll curLoc = 0;
	for (int l = L; l >= 0; l--) {
		if (curLoc + jumpDist[curLoc % N][l] <= N * K) {
			curLoc += jumpDist[curLoc % N][l];
		}
	}

	vector<int> ans;
	while (curLoc < N * K) {
		ll nxtLoc = (curLoc + jumpDist[curLoc % N][0]);
		if (nxtLoc <= N * K) {
			curLoc = nxtLoc;
		} else {
			ans.push_back(A[curLoc % N]);
			curLoc++;
		}
	}

	for (int v : ans) {
		printf("%d ", v);
	}
	printf("\n");

	return 0;
}
