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:
//check violation of constraints

import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.NoSuchElementException;

public class Main {

	void run(int N, int K, long[] H) {
		HashSet<Long> set = new HashSet<>();
		HashMap<Long, Integer> map = new HashMap<>();
		for (long h : H) {
			set.add(h);
		}
		set.add(0L);
		long[] hs = new long[set.size()];
		int p = 0;
		for (long h : set) {
			hs[p++] = h;
		}
		Arrays.sort(hs);
		for (int i = 0; i < hs.length; ++i)
			map.put(hs[i], i);
		long[][][] dp = new long[N + 1][set.size()][K + 1];
		for (int i = 0; i < N; ++i)
			for (int j = 0; j < set.size(); ++j)
				for (int k = 0; k <= K; ++k)
					dp[i][j][k] = Long.MAX_VALUE / 3;
		dp[0][map.get(H[0])][0] = H[0];
		for (int j = 0; j < set.size() && 1 <= K; ++j) {
			dp[0][j][1] = Math.min(dp[0][j][1], hs[j]);
		}
		for (int i = 1; i < N; ++i) {
			// Kを使用
			int me = map.get(H[i]);
			for (int k = 0; k + 1 <= K; ++k) {
				int mi = 0;
				for (int j = 0; j < set.size(); ++j) {
					if (dp[i - 1][mi][k] + Math.max(0, hs[j] - hs[mi]) >= dp[i - 1][j][k])
						mi = j;
					dp[i][j][k + 1] = Math.min(dp[i][j][k + 1], dp[i - 1][mi][k] + Math.max(0, hs[j] - hs[mi]));
				}
			}
			// Kを使用しない
			for (int k = 0; k <= K; ++k) {
				for (int j = 0; j < set.size(); ++j) {
					dp[i][me][k] = Math.min(dp[i][me][k], dp[i - 1][j][k] + Math.max(0, hs[me] - hs[j]));
				}
			}
		}
		long ans = Long.MAX_VALUE / 3;
		for (int k = 0; k <= K; ++k) {
			for (int j = 0; j < set.size(); ++j) {
				ans = Math.min(ans, dp[N - 1][j][k]);
			}
		}
		System.out.println(ans);
	}

	public static void main(String[] args) throws FileNotFoundException {
		FastScanner sc = new FastScanner();
		int N = sc.nextInt();
		int K = sc.nextInt();
		long[] H = new long[N];
		for (int i = 0; i < N; ++i)
			H[i] = sc.nextLong();
		new Main().run(N, K, H);
	}

	void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}
}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
		return hasNextByte();
	}

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
			throw new NumberFormatException();
		return (int) nl;
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}
}