Problem: 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.

Examples

Input

4 1
2 3 4 1


Output

3


Input

6 2
8 6 9 1 2 1


Output

7


Input

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


Output

4999999996

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.io.IOException;
import java.util.Random;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            TaskF solver = new TaskF();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class TaskF {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            int k = in.readInt();
            int[] hs = new int[n + 1];
            for (int i = 1; i <= n; i++) {
                hs[i] = in.readInt();
            }

            DiscreteMap dm = new DiscreteMap(hs.clone());
            for (int i = 0; i <= n; i++) {
                hs[i] = dm.rankOf(hs[i]);
            }

            int m = dm.maxRank();
            long[][][] dp = new long[n + 1][k + 1][m + 1];
            SequenceUtils.deepFill(dp, (long) 1e13);
            dp[0][0][0] = 0;
            long[][][] prefix = new long[n + 1][k + 1][m + 1];
            long[][][] suffix = new long[n + 1][k + 1][m + 1];
            for (int i = 0; i <= k; i++) {
                for (int j = 0; j <= m; j++) {
                    if (j == 0) {
                        prefix[0][i][j] = dp[0][i][j];
                    } else {
                        prefix[0][i][j] = Math.min(prefix[0][i][j - 1] + dm.iThElement(j) - dm.iThElement(j - 1), dp[0][i][j]);
                    }
                }

                for (int j = m; j >= 0; j--) {
                    if (j == m) {
                        suffix[0][i][j] = dp[0][i][j];
                    } else {
                        suffix[0][i][j] = Math.min(suffix[0][i][j + 1], dp[0][i][j]);
                    }
                }
            }
            for (int i = 1; i <= n; i++) {
                int h = hs[i];
                for (int j = 0; j <= k; j++) {
                    for (int t = 0; t <= m; t++) {
                        if (t != h) {
                            if (j > 0) {
                                dp[i][j][t] = Math.min(prefix[i - 1][j - 1][t], dp[i][j][t]);
                                dp[i][j][t] = Math.min(suffix[i - 1][j - 1][t], dp[i][j][t]);
                            } else {

                            }
                        } else {
                            dp[i][j][t] = Math.min(prefix[i - 1][j][t], dp[i][j][t]);
                            dp[i][j][t] = Math.min(suffix[i - 1][j][t], dp[i][j][t]);
                        }
                    }
                }

                for (int ii = 0; ii <= k; ii++) {
                    for (int jj = 0; jj <= m; jj++) {
                        if (jj == 0) {
                            prefix[i][ii][jj] = dp[i][ii][jj];
                        } else {
                            prefix[i][ii][jj] = Math.min(prefix[i][ii][jj - 1] + dm.iThElement(jj) - dm.iThElement(jj - 1), dp[i][ii][jj]);
                        }
                    }
                    for (int jj = m; jj >= 0; jj--) {
                        if (jj == m) {
                            suffix[i][ii][jj] = dp[i][ii][jj];
                        } else {
                            suffix[i][ii][jj] = Math.min(suffix[i][ii][jj + 1], dp[i][ii][jj]);
                        }
                    }


                }
            }

            long ans = (long) 1e18;
            for (int i = 0; i <= k; i++) {
                for (int j = 0; j <= m; j++) {
                    ans = Math.min(ans, dp[n][i][j]);
                }
            }

            out.println(ans);
        }

    }

    static class FastOutput implements AutoCloseable, Closeable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput println(long c) {
            cache.append(c).append('\n');
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class Randomized {
        static Random random = new Random();

        public static void randomizedArray(int[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                int tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static int nextInt(int l, int r) {
            return random.nextInt(r - l + 1) + l;
        }

    }

    static class DiscreteMap {
        int[] val;
        int f;
        int t;

        public DiscreteMap(int[] val) {
            this(val, 0, val.length);
        }

        public DiscreteMap(int[] val, int f, int t) {
            Randomized.randomizedArray(val, f, t);
            Arrays.sort(val, f, t);
            int wpos = f + 1;
            for (int i = f + 1; i < t; i++) {
                if (val[i] == val[i - 1]) {
                    continue;
                }
                val[wpos++] = val[i];
            }
            this.val = val;
            this.f = f;
            this.t = wpos;
        }

        public int rankOf(int x) {
            return Arrays.binarySearch(val, f, t, x) - f;
        }

        public int iThElement(int i) {
            return val[f + i];
        }

        public int maxRank() {
            return t - f - 1;
        }

        public String toString() {
            return Arrays.toString(Arrays.copyOfRange(val, f, t));
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class SequenceUtils {
        public static void deepFill(Object array, long val) {
            if (!array.getClass().isArray()) {
                throw new IllegalArgumentException();
            }
            if (array instanceof long[]) {
                long[] longArray = (long[]) array;
                Arrays.fill(longArray, val);
            } else {
                Object[] objArray = (Object[]) array;
                for (Object obj : objArray) {
                    deepFill(obj, val);
                }
            }
        }

    }
}