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()))

memo = {}
nxts = [None] * N
for i, x in enumerate(A + A):
  if x in memo:
    nxts[memo[x] % N] = i % N
  memo[x] = i

k = 0
visited = [-1] * N
p = 0
flag = False
ans = []
while k < K:
  if flag == False and visited[p] >= 0:
    vp = visited[p]
    k = vp + ((K-1) - vp) // (k - vp) * (k - vp)
    flag = True
  visited[p] = k
  nxt = nxts[p]
  if k == K-1 and nxt <= p:
    ans.append(A[p])
    nxt = p + 1
    if nxt >= N:
      break
  else:
    if nxt <= p:
      k += 1
    nxt = nxt + 1
    if nxt >= N:
      nxt %= N
      k += 1
  p = nxt

print(' ' .join(map(str, ans)))