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;

long a[222222], b[222222], t[222222], c[222222];
int main() {
	long n, k;
	cin >> n >> k;
	for (int i = 0; i < n; i++)
		scanf("%ld", a + i);
	for (int j = 2; j--;) {
		for (int i = n; i--;) {
			b[i] = t[a[i]];
			t[a[i]] = i + j * n;
		}
	}
	long x = 0;
	int y = 0;
	do {
		c[y++] = x;
		x = x / n * n + b[x%n] + 1;
	} while (x%n);
	x /= n;
	int l = lower_bound(c, c + y, k%x*n) - c - 1;
	for (l = c[l] % n; l < n; l++) {
		if (b[l] < n) l = b[l];
		else cout << a[l] << ' ';
	}
	cout << endl;
	return 0;
}
