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: import sys
  
  
  def input():
      return sys.stdin.readline().strip()
  
  
  def mapint():
      return map(int, input().split())
  
  
  sys.setrecursionlimit(10**9)
  
  N, K = mapint()
  As = list(mapint())
  double_As = As * 2
  idx_dic = {}
  idx_lis = [N + 1] * (2 * N)
  for i in range(N * 2 - 1, -1, -1):
      a = double_As[i]
      if a in idx_dic:
          idx_lis[i] = idx_dic[a] + 1
      idx_dic[a] = i
  doubling = [[0] * N for _ in range(60)]
  accum = [[0] * N for _ in range(60)]
  doubling[0] = [i % N for i in idx_lis[:N]]
  accum[0] = [a - i for i, a in enumerate(idx_lis[:N])]
  for i in range(1, 60):
      for j in range(N):
          doubling[i][j] = doubling[i - 1][doubling[i - 1][j]]
          accum[i][j] = accum[i - 1][j] + accum[i - 1][doubling[i - 1][j]]
  now = 0
  cum = 0
  cnt = 0
  for i in range(59, -1, -1):
      if cum + accum[i][now] > N * K:
          continue
      else:
          cum += accum[i][now]
          now = doubling[i][now]
  ans = []
  while cum < N * K:
      if cum + accum[0][now] <= N * K:
          cum += accum[0][now]
          now = doubling[0][now]
      else:
          ans.append(As[now])
          now += 1
          cum += 1
  print(*ans)
  
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"}]