Problem:
Score : 600 points

Problem 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.

Constraints

1 \leq N \leq 300

0 \leq K \leq N

0 \leq H_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
H_1 H_2 ... H_N

Output

Print the minimum number of operations required.

Sample Input 1

4 1
2 3 4 1

Sample Output 1

3

For example, by changing the value of H_3 to 2, you can create the modified artwork by the following three operations:

Paint black the 1-st through 4-th squares from the left in the 1-st row from the bottom.

Paint black the 1-st through 3-rd squares from the left in the 2-nd row from the bottom.

Paint black the 2-nd square from the left in the 3-rd row from the bottom.

Sample Input 2

6 2
8 6 9 1 2 1

Sample Output 2

7

Sample Input 3

10 0
1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000

Sample Output 3

4999999996

Solution in Scala (2.11.7) (judge verdict: Wrong Answer)

import java.io.PrintWriter

object Loop {
  @inline def rep(n: Int, f: => Unit): Unit = { var c = 0; while (c < n) { f; c += 1 } }
  @inline def rep(n: Int, f: Int => Unit): Unit = { var c = 0; while (c < n) { f(c); c += 1 } }

  @inline def breakAble(n: Int, m: Int, f: Int => Boolean): Unit = if (f(n) && n < m) breakAble(n + 1, m, f)
  @inline def !(n: Int): Int = (1 + n) * n / 2
}
object Mod {
  def create(n: Int, mod: Int) = Mod(n, mod)
}
case class Mod(n: Int, mod: Int) {
  val factorial: Array[Int] = Array.fill[Int](n + 1)(1)
  val inverse: Array[Int] = Array.fill[Int](n + 1)(1)
  val inverseFactorial: Array[Int] = Array.fill[Int](n + 1)(1)
  Loop.rep(n - 1, i => {
    val k = i + 2
    factorial(k) = modMultiplyExact(factorial(k - 1), k, mod)
    inverse(k) = modMultiplyExact(inverse(mod % k), mod - (mod / k): Int, mod)
    inverseFactorial(k) = modMultiplyExact(inverseFactorial(k - 1), inverse(k), mod)
  })
  def getFactorial(n: Int): Int = factorial(n)
  def getInverse(n: Int): Int = inverse(n)
  def getInverseFactorial(n: Int): Int = inverseFactorial(n)
  def C(n: Int, k: Int): Int = {
    if (n <= 0 || k < 0 || k > n) 0 else if (k == 0 || k == n) 1 else {
      modMultiplyExact(
        getFactorial(n),
        getInverseFactorial(n - k),
        getInverseFactorial(k),
        mod
      )
    }
  }
  def modMultiplyExact(a: Int, b: Int, m: Int): Int =
    ((a.toLong * b.toLong) % m).toInt
  def modMultiplyExact(a: Int, b: Int, c: Int, m: Int): Int =
    modMultiplyExact(a, modMultiplyExact(b, c, m), m)
}
object Scanner {
  private val buf = new Array[Byte](1024); private var ptr = 0; private var len = 0
  @inline private def isPrintableChar(c: Int): Boolean = 33 <= c && c <= 126
  @inline private def hasNextByte(): Boolean =
    if (ptr >= len) { ptr = 0; len = System.in.read(buf); len > 0 } else { true }
  @inline private def hasNext(): Boolean = {
    while (hasNextByte() && !isPrintableChar(buf(ptr))) ptr += 1
    hasNextByte()
  }
  @inline private def readByte(): Byte =
    if (hasNextByte()) { val res = buf(ptr); ptr += 1; res } else { -1 }
  def next(): String = {
    if(!hasNext()) ???
    val sb = new StringBuilder; var b = readByte()
    while (isPrintableChar(b)) { sb.append(b.toChar); b = readByte() }
    sb.toString
  }
  def nextInt(): Int = {
    val n = nextLong()
    if (n < Int.MinValue || Int.MaxValue < n) ???
    n.toInt
  }
  def nextLong(): Long = {
    if(!hasNext()) ???
    var minus = false; var b = readByte()
    if (b == '-') { minus = true; b = readByte() }
    def go (b: Byte, n: Long = 0): Long =
      if ('0' <= b && b <= '9') { go(readByte(), n * 10 + b - '0') }
      else if (minus) { -n } else { n }
    go(b)
  }
  def nextDouble(): Double = next.toDouble

  def print(f:PrintWriter => Unit): Unit = {
    val pw: PrintWriter = new java.io.PrintWriter(System.out)
    //pw.println("")
    f(pw)
    pw.flush()
  }
}
////////////////////////////////////////
//
////////////////////////////////////////
object Main extends App {
  val n, k = Scanner.nextInt()
  val data = Array.fill(n)(Scanner.nextLong())
  val dp = Array.fill[Long](n + 1, n + 1)(-1)

  def pure(i: Int, k: Int, x: Long): Long = {
    val d = dp(i)(k)
    if (d >= 0) d else {
      val r =
        if (i == 0) {
          0
        } else if (i == k) {
          0
        } else if (k > 0) {
          val x1 = data(i - 1)
          val count = Math.max(0, x1 - x)
          val leave = count + pure(i - 1, k, x1)
          val erase = pure(i - 1, k - 1, x)
          Math.min(erase, leave)
        } else {
          val x1 = data(i - 1)
          val count = Math.max(0, x1 - x)
          val leave = count + pure(i - 1, k, x1)
          leave
        }
      dp(i)(k) = r
      r
    }
  }
  println(pure(n, k, 0))
}