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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ABC145.F();
        }



        class ABC145
        {
            public static void A()
            {
                var R = Read.Int();
                Console.WriteLine(R * R);
            }
            public static void B()
            {
                var N = Read.Int();
                var S = Read.Str();
                Console.WriteLine(N % 2 == 0 && S.Substring(0, N / 2) == S.Substring(N / 2, N / 2) ? "Yes" : "No");
            }
            public static void C()
            {
                var N = Read.Int();
                var XY = Read.TupleInt(N);
                double sum = 0;
                for(int i = 0; i < N; ++i)
                {
                    var x1 = XY[i].Item1;
                    var y1 = XY[i].Item2;
                    for (int j = i + 1; j < N; ++j)
                    {
                        var x2 = XY[j].Item1;
                        var y2 = XY[j].Item2;
                        sum += Math.Sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
                    }
                }
                Console.WriteLine(sum / N * 2);
            }
            public static void D()
            {
                var X = Read.Int();
                var Y = Read.Int();
                if ((X + Y) % 3 != 0) { Console.WriteLine(0);return; }
                var a = X - (X + Y) / 3;
                var b = Y - (X + Y) / 3;
                Console.WriteLine(Util.Combin(a + b, 1000000007)(a + b, a));
            }
            public static void E()
            {
                var N = Read.Int();
                var T = Read.Int();
                var AB = Read.TupleInt(N);
                AB = AB.OrderBy(x => x.Item1).ToArray();
                var dp = new int[N + 1, T];
                for(int n = 0; n < N; ++n)
                {
                    var A = AB[n].Item1;
                    var B = AB[n].Item2;
                    for(int t = 0; t < T; ++t)
                    {
                        if (t >= A)
                        {
                            dp[n + 1, t] = Math.Max(dp[n, t], dp[n, t - A] + B);
                        }
                        else
                        {
                            dp[n + 1, t] = dp[n, t];
                        }
                    }
                }
                int max = 0;
                int maxB = 0;
                for(int n = N; n > 0; --n)
                {
                    max = Math.Max(max, dp[n, T - 1] + maxB);
                    maxB = Math.Max(maxB, AB[n - 1].Item2);
                }
                Console.WriteLine(max);
            }
            public static void F()
            {
                var N = Read.Int();
                var K = Read.Int();
                var H = Read.LongN();
                H = new long[] { 0 }.Concat(H).ToArray();
                var dp = new long[N + 1, N - K + 1];
                for (int len = 0; len <= N - K; ++len)
                {
                    dp[0, len] = len == 0 ? 0 : (long)1e18;
                }
                for (int n = 1; n <= N; ++n)
                {
                    dp[n, 0] = (long)1e18;
                    var h = H[n];
                    for(int len = 1; len <= N - K; ++len)
                    {
                        long min = (long)1e18;
                        for(int prev = 0; prev < n; ++prev)
                        {
                            min = Math.Min(min, dp[prev, len - 1] + Math.Max(0, h - H[prev]));
                        }
                        dp[n, len] = min;
                    }
                }
                Console.WriteLine(Enumerable.Range(1, N).Select(n => dp[n, N - K]).Min());
            }
        }


        class Util
        {
            public static long Inverse(long a, long p)
            {
                long b = p, c = 1, d = 0, e = 0, f = 0;
                while (b != 0)
                {
                    e = a / b;
                    f = b; b = a - e * b; a = f;
                    f = d; d = c - e * d; c = f;
                }
                c %= p;
                return c + (c < 0 ? p : 0);
            }

            public static long[] Facts(int n, long p)
            {
                var facts = new long[n + 1];
                facts[0] = 1;
                for (int i = 1; i <= n; ++i)
                {
                    facts[i] = (i * facts[i - 1]) % p;
                }
                return facts;
            }
            public static Func<int, int, long> Combin(int n, long P)
            {
                var fact = Facts(n, P);
                var inv = fact.Select(x => Inverse(x, P)).ToArray();
                return (N, M) =>
                {
                    if (N < 0 || N < M || M < 0) { return 0; }
                    return (((fact[N] * inv[M]) % P) * inv[N - M]) % P;
                };
            }
        }


        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN(); dict[ab[0]].Add(ab[1]);
                    if (!isDirectional) { dict[ab[1]].Add(ab[0]); }
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}