output_description: Print the elements of s after Snuke finished the operations, in order from
  beginning to end, with spaces in between.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N K
      A_0 A_1 \cdots A_{N-1}
attempt: from collections import defaultdict
  
  n, k = list(map(int, input().split()))
  a = list(map(int, input().split()))
  
  t = set()
  tt = []
  ttt = defaultdict(int)
  
  tttt = defaultdict(int)
  for i in range(n - 1, -1, -1):
      tttt[a[i]] = i
  
  s = []
  
  for i in range(n):
      if ttt[a[i % n]] == 0:
          s.append(a[i % n])
          ttt[a[i % n]] += 1
      else:
          while ttt[a[i % n]] > 0:
              ttt[s.pop()] -= 1
      if i % n == n - 1:
          # print(s)
          if tuple(s) in t:
              want = tuple(s)
              break
          t.add(tuple(s))
          tt.append(tuple(s))
  
  
  for i in range(k - 1):
      if len(s) == 0:
          want = tt[0]
          break
      if len(s):
          s = a[tttt[s[0]] + 1 :]
          ss = []
          ttttt = defaultdict(lambda: -1)
          for j in range(len(s)):
              if ttttt[s[j]] != -1:
                  ss.extend(s[: ttttt[s[j]]])
                  ss.extend(s[j + 1 :])
                  ttttt[s[j]] = -1
              else:
                  ttttt[s[j]] = j
          s = ss
      # print(s)
      if tuple(s) in t:
          want = tuple(s)
          break
      t.add(tuple(s))
      tt.append(tuple(s))
  
  # print(t)
  # print(tt)
  # print(want)
  
  if len(tt) == k:
      print(*tt[-1])
  else:
      idx = 0
      for i in range(len(tt)):
          if tt[i] == want:
              idx = i
      # print(want, idx)
      print(*tt[k % (len(tt) - idx) - 1])
  
problem_description: Statement
  
  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.
samples: [{"input": "3 2\n    1 2 3", "output": "2 3\n    \n\nIn this case, X=(1,2,3,1,2,3). We will perform the operations as follows:\n\n  * i=0: s does not contain 1, so we add 1 to the end of s, resulting in s=(1).\n  * i=1: s does not contain 2, so we add 2 to the end of s, resulting in s=(1,2).\n  * i=2: s does not contain 3, so we add 3 to the end of s, resulting in s=(1,2,3).\n  * i=3: s does contain 1, so we repeatedly delete the element at the end of s as long as s contains 1, which causes the following changes to s: (1,2,3)\u2192(1,2)\u2192(1)\u2192().\n  * i=4: s does not contain 2, so we add 2 to the end of s, resulting in s=(2).\n  * i=5: s does not contain 3, so we add 3 to the end of s, resulting in s=(2,3).\n\n* * *"}, {"input": "5 10\n    1 2 3 2 3", "output": "3\n    \n\n* * *"}, {"input": "6 1000000000000\n    1 1 2 2 3 3", "output": "s may be empty in the end.\n\n* * *"}, {"input": "11 97\n    3 1 4 1 5 9 2 6 5 3 5", "output": "9 2 6"}]