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
import sys
n, k = map(int, input().split())
a = list(map(int, input().split()))
if n == 1:
	if k%2 == 1:
		print(a[0])
	else:
		print("")
else:
	aa = a + a
	skip = [0 for _ in range(n)]
	ind = dict()
	for i in range(2*n-1, -1, -1):
		if aa[i] in ind and i < n:
			skip[i] = ind[aa[i]]-i+1
		ind[aa[i]] = i
	#print(skip)
	if k == 1:
		ans = []
		cnt = 0
		while cnt < n:
			if cnt + skip[cnt%n] > n:
				ans.append(a[cnt])
				cnt += 1
			elif cnt + skip[cnt%n] <= n:
				cnt += skip[cnt%n]
		print(*ans)
		sys.exit()
	cnt = 0
	while cnt == 0 or (cnt + skip[cnt%n] <= n*k and cnt%n != 0):
		cnt += skip[cnt%n]
	if cnt%n == 0:
		l = cnt//n
		#print(l)
		k %= l
		if k == 0:
			print("")
			sys.exit()
		cnt = 0
		while cnt == 0 or cnt + skip[cnt%n] <= n*k:
			cnt += skip[cnt%n]
	ans = []
	cnt = cnt%n
	while cnt < n:
		if cnt + skip[cnt%n] > n:
			ans.append(a[cnt])
			cnt += 1
		elif cnt + skip[cnt%n] <= n:
			cnt += skip[cnt%n]
	print(*ans)