output_description: Print the minimum number of operations required.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N K
      H_1 H_2 ... H_N
attempt: N, K = map(int, input().split())
  
  H = list(map(int, input().split()))
  
  HSorted = sorted(H)
  
  HIndexToHeight = []
  HHeightToIndex = {}
  
  for i in range(N):
      if i != 0 and HSorted[i] == HSorted[i - 1]:
          continue
      HIndexToHeight.append(HSorted[i])
      HHeightToIndex[HSorted[i]] = len(HIndexToHeight) - 1
  
  INF = 10**12
  
  heightCount = len(HIndexToHeight)
  
  DP = []
  for i in range(N):
      DP.append([])
      for j in range(K + 1):
          DP[i].append([])
          for k in range(heightCount):
              DP[i][j].append(INF)
  
  for k in range(heightCount):
      if k == HHeightToIndex[H[0]]:
          DP[0][0][k] = H[0]
      else:
          DP[0][1][k] = HIndexToHeight[k]
  
  for i in range(1, N):
      currentHeight = HHeightToIndex[H[i]]
      for j in range(K + 1):
          for k in range(heightCount):
              if currentHeight > k:
                  if j > 0:
                      DP[i][j][k] = min(DP[i - 1][j - 1][k], DP[i][j][k])
                  DP[i][j][currentHeight] = min(
                      DP[i - 1][j][k] + HIndexToHeight[currentHeight] - HIndexToHeight[k],
                      DP[i][j][currentHeight],
                  )
              elif currentHeight == k:
                  DP[i][j][currentHeight] = min(DP[i - 1][j][k], DP[i][j][currentHeight])
              else:
                  if j > 0:
                      DP[i][j][k] = min(DP[i - 1][j - 1][k], DP[i][j][k])
                  DP[i][j][currentHeight] = min(DP[i - 1][j][k], DP[i][j][currentHeight])
  ans = INF
  
  for j in range(K + 1):
      for k in range(heightCount):
          if ans > DP[N - 1][j][k]:
              ans = DP[N - 1][j][k]
  
  print(ans)
  
problem_description: Statement
  
  We will create an artwork by painting black some squares in a white square
  grid with 10^9 rows and N columns.  
  The current plan is as follows: for the i-th column from the left, we will
  paint the H_i bottommost squares and will not paint the other squares in that
  column.  
  Before starting to work, you can choose at most K columns (possibly zero) and
  change the values of H_i for these columns to any integers of your choice
  between 0 and 10^9 (inclusive).  
  Different values can be chosen for different columns.  
  
  Then, you will create the modified artwork by repeating the following
  operation:  
  
    * Choose one or more consecutive squares in one row and paint them black. (Squares already painted black can be painted again, but squares not to be painted according to the modified plan should not be painted.)
  
  Find the minimum number of times you need to perform this operation.
samples: [{"input": "4 1\n    2 3 4 1", "output": "3\n    \n\nFor example, by changing the value of H_3 to 2, you can create the modified\nartwork by the following three operations:\n\n  * Paint black the 1-st through 4-th squares from the left in the 1-st row from the bottom.\n  * Paint black the 1-st through 3-rd squares from the left in the 2-nd row from the bottom.\n  * Paint black the 2-nd square from the left in the 3-rd row from the bottom.\n\n* * *"}, {"input": "6 2\n    8 6 9 1 2 1", "output": "7\n    \n\n* * *"}, {"input": "10 0\n    1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000", "output": "4999999996"}]