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 collections import defaultdict
from bisect import bisect_right
N,K,*A = map(int, open(0).read().split())
a = A[0]
p = 0
ls = []
dic = defaultdict(list)
for i,c in enumerate(A):
  dic[c].append(i)
while True:
  ls.append(p)
  ind = bisect_right(dic[a],p%N)
  if ind==len(dic[a]):
    ind = 0
    p += N
  p = (p//N)*N+dic[a][ind]+1
  if p%N==0:
    M = p//N
    break
  a = A[p%N]
K %= M
X = N*K
I = bisect_right(ls,X)-1
X -= ls[I]
p = ls[I]%N
S = set()
cnt = 0
ans = []
while X:
  if A[p] not in S:
    S.add(A[p])
    ans.append(A[p])
    cnt += 1
  else:
    i = ans.index(A[p])
    ans = ans[:i]
    S = set(ans)
    cnt = i
  X -= 1
  p += 1
  p %= N
print(' '.join(map(str,ans)))    