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
N,K = map(int, input().split())
A = list(map(int,input().split()))
MAX = 2 * 10**5+1
nxt = [-1 for i in range(MAX)]

last_index = [-1 for i in range(MAX)]
next_index = [-1 for i in range(MAX)]
first_index = [-1 for i in range(MAX)]
for i in range(N):
	a = A[i]
	last = last_index[a]
	if last >= 0:
		next_index[last] = i
	else:
		first_index[a] = i
	last_index[a] = i

start_stat = 0
while True:
	current = first_index[start_stat] + 1
	while current < N and next_index[current] != -1:
		current = next_index[current] + 1
	if current >= N:
		nxt[start_stat] = 0
		break
	else:
		stat = A[current]
		nxt[start_stat] = A[current]
		if nxt[A[current]] == -1:
			start_stat = A[current]
			continue
		else:
			break

order = [0]
in_order = [False for i in range(MAX)]
in_order[0] = True
last_stat = nxt[0]
while not in_order[last_stat]:
	order.append(last_stat)
	in_order[last_stat] = True
	last_stat = nxt[last_stat]
a,b = 0,len(order)
for x in order:
	if x == last_stat:
		break
	else:
		a += 1
		b -= 1
stat_index = K if K < a else (K-a) % b
init_status = order[stat_index]
before_stat = order[(stat_index - 1) % len(order)]
current = first_index[before_stat] + 1
if init_status == 0:
	print("")
	exit()
ans = []
while current < N:
	if next_index[current] != -1:
		current = next_index[current] + 1
	else:
		ans.append(A[current])
		current += 1
print( " ".join(list(map(str, ans))))
