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: def solve():
      N, K = map(int, input().split())
      As = list(map(int, input().split()))
  
      def getDistNexts(As):
          lenA = len(As)
          poss = dict()
          for i, A in enumerate(As):
              if A not in poss:
                  poss[A] = i + lenA
  
          distNexts = [0] * (lenA)
          for i in reversed(range(lenA)):
              distNexts[i] = poss[As[i]] - i
              poss[As[i]] = i
          return distNexts
  
      distNexts = getDistNexts(As)
  
      NK = N * K
      maxD = (NK).bit_length() - 1
  
      dp = [[0] * (N) for _ in range(maxD + 1)]
      for i in range(N):
          dp[0][i] = distNexts[i] + 1
      for d in range(1, maxD + 1):
          for i in range(N):
              i2 = i + dp[d - 1][i]
              dp[d][i] = i2 + dp[d - 1][i2 % N] - i
  
      iNow = 0
      dist = 0
      for d in reversed(range(maxD + 1)):
          if dist + dp[d][iNow] < NK:
              dist += dp[d][iNow]
              iNow = dist % N
  
      Ss = []
      setS = set()
      for A in As[iNow:]:
          if A in setS:
              S = ""
              while S != A:
                  S = Ss.pop()
                  setS.remove(S)
          else:
              Ss.append(A)
              setS.add(A)
  
      if Ss:
          print(" ".join(map(str, Ss)))
  
  
  solve()
  
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"}]