output_description: Print the minimum number of the Teleporters whose destinations need to be
  changed in order to satisfy King Snuke's desire.
  
  * * *
input_description: The input is given from Standard Input in the following format:
  
      
      
      N K
      a_1 a_2 ... a_N
attempt: import sys
  
  INF = 1 << 60
  MOD = 10**9 + 7  # 998244353
  sys.setrecursionlimit(2147483647)
  input = lambda: sys.stdin.readline().rstrip()
  
  
  def resolve():
      n, k = map(int, input().split())
      f = list(map(lambda x: int(x) - 1, input().split()))
  
      # f(0) = 0 is necessary
      ans = 0 + (f[0] != 0)
      f[0] = -1
  
      # we regard f as 0 rooted tree except for an edge 0 -> 0
      E = [[] for _ in range(n)]
      indeg = [0] * n
      for i in range(1, n):
          E[f[i]].append(i)
          indeg[i] += 1
  
      # topological sort
      stack = [0]
      order = []
      while stack:
          v = stack.pop()
          order.append(v)
          for nv in E[v]:
              stack.append(nv)
      order.reverse()
  
      dp = [-1] * n
      for v in order:
          res = 0
          for nv in E[v]:
              res = max(res, (dp[nv] + 1) % k)
          dp[v] = res
  
      ans += dp.count(k - 1)
      if dp[0] == k - 1:
          ans -= 1
      for v in E[0]:
          if dp[v] == k - 1:
              ans -= 1
      print(ans)
  
  
  resolve()
  
problem_description: Statement
  
  There are N towns in Snuke Kingdom, conveniently numbered 1 through N. Town 1
  is the capital.
  
  Each town in the kingdom has a _Teleporter_ , a facility that instantly
  transports a person to another place. The destination of the Teleporter of
  town i is town a_i (1≤a_i≤N). It is guaranteed that **one can get to the
  capital from any town by using the Teleporters some number of times**.
  
  King Snuke loves the integer K. The selfish king wants to change the
  destination of the Teleporters so that the following holds:
  
    * Starting from any town, one will be at the capital after using the Teleporters exactly K times in total.
  
  Find the minimum number of the Teleporters whose destinations need to be
  changed in order to satisfy the king's desire.
samples: [{"input": "3 1\n    2 3 1", "output": "2\n    \n\nChange the destinations of the Teleporters to a = (1,1,1).\n\n* * *"}, {"input": "4 2\n    1 1 2 2", "output": "0\n    \n\nThere is no need to change the destinations of the Teleporters, since the\nking's desire is already satisfied.\n\n* * *"}, {"input": "8 2\n    4 1 2 3 1 2 3 4", "output": "3\n    \n\nFor example, change the destinations of the Teleporters to a =\n(1,1,2,1,1,2,2,4)."}]