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 bisect
from collections import defaultdict
n,k = map(int,input().split())
a = list(map(int,input().split()))
dc = defaultdict(int)
for i in range(n):
  if dc[a[i]]:
    dc[a[i]].append(i)
  else:
    dc[a[i]] = [i]
p = 0
cnt = 1
dcp = defaultdict(int)
while p != n and cnt<k:
  x = a[p]
  if p == dc[x][-1]:
    p = dc[x][0]+1
    cnt += 1
    dcp[cnt] = p
  else:
    q = bisect.bisect_right(dc[x],p)
    p = dc[x][q]+1
if cnt<k:
  k = k%cnt
ans = []
pos = dcp[k]
flg = [0 for i in range(200000+1)]
for i in range(pos,n):
  if flg[a[i]] == 0:
    ans.append(a[i])
    flg[a[i]] = 1
  else:
    while ans[-1] != a[i]:
      t = ans.pop()
      flg[t] = 0
    ans.pop()
    flg[a[i]] = 0
print(*ans)