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
from bisect import bisect
from collections import defaultdict
def main():
	n, k = map(int, input().split())
	*a, = map(int, input().split())
	idx = defaultdict(list)
	for i, x in enumerate(a):
		idx[x].append(i)
	m = (k * n).bit_length()
	dub = [[-1] * n for _ in range(m)]
	for i, x in enumerate(a):
		if i == idx[x][-1]:
			dub[0][i] = n + idx[x][0] - i
		else:
			dub[0][i] = idx[x][bisect(idx[x], i)] - i
	# print(dub[0])
	for i in range(m - 1):
		for j in range(n):
			if dub[i][j]<n*k and dub[i][j]!=-1:
				dub[i + 1][j] = dub[i][j] + 1 + dub[i][(j + dub[i][j] + 1) % n]
	# print(dub)
	now = -1
	for i in range(m - 1, -1, -1):
		if dub[i][(now+1)%n]!=-1 and now + 1 + dub[i][(now + 1) % n] < n * k:
			now += 1 + dub[i][(now + 1) % n]
	# print(now)
	if now == n * k:
		print("")
		exit()
	b = a[(now + 1) % n:]
	# print(b)
	inQ = {x: False for x in b}
	Q = []
	for x in b:
		if inQ[x]:
			while Q[-1] != x:
				inQ[Q.pop()] = False
			Q.pop()
			inQ[x] = False
		else:
			inQ[x] = True
			Q.append(x)
	print(" ".join(map(str, Q)))

if __name__ == '__main__':
	main()
