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 collections

n,k=map(int,input().split())
arr=list(map(int,input().split()))
pos=[[] for _ in range(max(arr)+1)]
for i in range(2*n):
  pos[arr[i%n]].append(i)
edge=[[] for _ in range(n)]
cnt=collections.defaultdict(int)
for i in range(n):
  s=pos[arr[i]][cnt[arr[i]]]
  g=pos[arr[i]][cnt[arr[i]]+1]
  edge[s].append((g+1)%n)
  edge[s].append((g+1)//n)
  cnt[arr[i]]+=1
start=0
loop=0
for _ in range(n):
  loop+=edge[start][1]
  start=edge[start][0]
  if start==0:
    break
k%=loop
if k==0:
  print('')
else:
  k-=1
  start=0
  loop=0
  for _ in range(n):
    if loop==k:
      break
    loop+=edge[start][1]
    start=edge[start][0]
  s=set()
  q=collections.deque()
  for i in range(start,n):
    if arr[i] not in s:
      s.add(arr[i])
      q.append(arr[i])
    else:
      while 1:
        tmp=q.pop()
        s.discard(tmp)
        if tmp==arr[i]:
          break
  print(*list(q))