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
from collections import defaultdict as dd
from bisect import bisect_left as bl
input = sys.stdin.readline
N, K = map(int, input().split())
a = list(map(int, input().split()))
dp = [0] * (N + 1)
d = dd(list)
for i in range(N):
  d[a[i]].append(i)
for i in range(N - 1, -1, -1):
  j = bl(d[a[i]], i)
  if j == len(d[a[i]]) - 1:
    dp[i] = a[i]
  else:
    dp[i] = dp[d[a[i]][j + 1] + 1]
p = dp[0]
t = 1
l = [0, dp[0]]
if l[-1] == 0:
  t -= 1
  l.pop()
d[0].append(-1)
for _ in range(N):
  p = dp[d[p][0] + 1]
  t += 1
  if p == 0: break
  l.append(p)
p = l[(K - 1) % t]
i = d[p][0] + 1
res = []
while i < N:
  j = bl(d[a[i]], i)
  if j < len(d[a[i]]) - 1:
    i = d[a[i]][j + 1]
  else:
    res.append(a[i])
  i += 1
print(*res)