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++14 (GCC 5.4.1) (judge verdict: Accepted)

#define _USE_MATH_DEFINES
#ifdef __GNUC__
#include <bits/stdc++.h>
#else
#define _CRT_SECURE_NO_WARNINGS
#include <__msvc_all_public_headers.hpp>
#undef min
#undef max
#endif
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define FOR(i, m, n) for (int i = (m); i < (n); ++i)
#define rrep(i, n) for (int i = (n) - 1; i >= 0; --i)
#define rfor(i, m, n) for (int i = (m); i >= (n); --i)
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define range_it(a, l, r) (a).begin() + (l), (a).begin() + (r)

using namespace std;
using ll = long long;		using ld = long double;
using VB = vector<bool>;	using VVB = vector<VB>;
using VI = vector<int>;		using VVI = vector<VI>;
using VL = vector<ll>;		using VVL = vector<VL>;
using VS = vector<string>;	using VD = vector<ld>;
using PII = pair<int, int>;	using VP = vector<PII>;
using PLL = pair<ll, ll>;	using VPL = vector<PLL>;
template<class T>using PQ = priority_queue<T>;
template<class T>using PQS = priority_queue<T, vector<T>, greater<T>>;
constexpr int inf = (int)1e9;
constexpr ll inf_ll = (ll)1e18, MOD = 1000000007;
constexpr ld PI = M_PI, EPS = 1e-12;

// --- input --- //
#ifdef _WIN32
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#define fwrite_unlocked _fwrite_nolock
#define fflush_unlocked _fflush_nolock
#endif
inline int gc() { return getchar_unlocked(); }
template<class T>inline void InputF(T& v) { cin >> v; }
inline void InputF(char& v) { while (isspace(v = gc())); }
inline void InputF(bool& v) { char c; InputF(c); v = c != '0'; }
inline void InputF(string& v) {
	char c; for (InputF(c); !isspace(c); c = gc())v += c;
}
inline void InputF(int& v) {
	bool neg = false; v = 0; char c; InputF(c);
	if (c == '-') { neg = true; c = gc(); }
	for (; isdigit(c); c = gc())v = v * 10 + (c - '0');
	if (neg)v = -v;
}
inline void InputF(long long& v) {
	bool neg = false; v = 0; char c; InputF(c);
	if (c == '-') { neg = true; c = gc(); }
	for (; isdigit(c); c = gc())v = v * 10 + (c - '0');
	if (neg)v = -v;
}
inline void InputF(double& v) {
	double dp = 1; bool neg = false, adp = false; v = 0; char c; InputF(c);
	if (c == '-') { neg = true; c = gc(); }
	for (; isdigit(c) || c == '.'; c = gc()) {
		if (c == '.')adp = true;
		else if (adp)v += (c - '0') * (dp *= 0.1);
		else v = v * 10 + (c - '0');
	}
	if (neg)v = -v;
}
template<class T, class U>inline void InputF(pair<T, U>& v) {
	InputF(v.first); InputF(v.second);
}
template<class T>inline void InputF(vector<T>& v) {
	for (auto& e : v)InputF(e);
}
template<class T>inline T InputF() { T v; InputF(v); return v; }
inline string GetLine() {
	string v; char c; for (InputF(c); c != '\n' && c != '\0'; c = gc())v += c; return v;
}
struct InputV {
	int n, m;
	InputV(int N) :n(N), m(0) {}
	InputV(pair<int, int> N) :n(N.first), m(N.second) {}
	template<class T>operator vector<T>() {
		vector<T> v(n); InputF(v); return v;
	}
	template<class T>operator vector<vector<T>>() {
		vector<vector<T>> v(n, vector<T>(m)); InputF(v); return v;
	}
};
struct Input {
	template<class T>operator T() { return InputF<T>(); }
	int operator--(int) { int v; InputF(v); v--; return v; }
	InputV operator[](int n) { return InputV(n); }
	InputV operator[](pair<int, int> n) { return InputV(n); }
	void operator()() {}
	template<class H, class...T>void operator()(H&& h, T&& ...t) {
		InputF(h); operator()(forward<T>(t)...);
	}
	template<class T>Input& operator,(T&& v) {
		InputF(v); return *this;
	}
}in;
#define input(T) InputF<T>()
#define ini input(int)
#define inl input(ll)
#define ins input(string)
#define inputs(T, ...) T __VA_ARGS__; in(__VA_ARGS__)
#define INT(...) inputs(int, __VA_ARGS__)
#define LL(...) inputs(ll, __VA_ARGS__)
#define STR(...) inputs(string, __VA_ARGS__)

// --- output --- //
struct BoolStr {
	const char* t, * f; BoolStr(const char* _t, const char* _f) :t(_t), f(_f) {}
}Yes("Yes", "No"), yes("yes", "no"), YES("YES", "NO"), Int("1", "0");
struct DivStr {
	const char* d, * l; DivStr(const char* _d, const char* _l) :d(_d), l(_l) {}
}spc(" ", "\n"), no_spc("", "\n"), end_line("\n", "\n"), comma(",", "\n"), no_endl(" ", "");
class Output {
	BoolStr B{ Yes }; DivStr D{ spc };
	void p(int v) {
		if (v < 0)putchar_unlocked('-'), v = -v;
		char b[10]; int i = 0;
		while (v)b[i++] = '0' + v % 10, v /= 10;
		if (!i)b[i++] = '0';
		while (i--)putchar_unlocked(b[i]);
	}
	void p(ll v) {
		if (v < 0)putchar_unlocked('-'), v = -v;
		char b[20]; int i = 0;
		while (v)b[i++] = '0' + v % 10, v /= 10;
		if (!i)b[i++] = '0';
		while (i--)putchar_unlocked(b[i]);
	}
	void p(bool v) { p(v ? B.t : B.f); }
	void p(char v) { putchar_unlocked(v); }
	void p(const char* v) { fwrite_unlocked(v, 1, strlen(v), stdout); }
	void p(double v) { printf("%.20f", v); }
	void p(ld v) { printf("%.20Lf", v); }
	template<class T> void p(const T& v) { cout << v; }
	template<class T, class U>void p(const pair<T, U>& v) { p(v.first); p(D.d); p(v.second); }
	template<class T>void p(const vector<T>& v) { rep(i, sz(v)) { if (i)p(D.d); p(v[i]); } }
	template<class T>void p(const vector<vector<T>>& v) { rep(i, sz(v)) { if (i)p(D.l); p(v[i]); } }
public:
	Output& operator()() { p(D.l); return *this; }
	template<class H>Output& operator()(H&& h) { p(h); p(D.l); return *this; }
	template<class H, class...T>Output& operator()(H&& h, T&& ...t) {
		p(h); p(D.d); return operator()(forward<T>(t)...);
	}
	template<class...T>void exit(T&& ...t) { operator()(forward<T>(t)...); std::exit(EXIT_SUCCESS); }
	Output& flush() { fflush_unlocked(stdout); return *this; }
	Output& set(const BoolStr& b) { B = b; return *this; }
	Output& set(const DivStr& d) { D = d; return *this; }
	Output& set(const char* t, const char* f) { B = BoolStr(t, f); return *this; }
}out;

// --- step --- //
template<class T>struct Step {
	class It {
		T a, b, c;
	public:
		constexpr It() : a(T()), b(T()), c(T()) {}
		constexpr It(T _b, T _c, T _s) : a(_b), b(_c), c(_s) {}
		constexpr It& operator++() { --b; a += c; return *this; }
		constexpr It operator++(int) { It tmp = *this; --b; a += c; return tmp; }
		constexpr const T& operator*()const { return a; }
		constexpr const T* operator->()const { return &a; }
		constexpr bool operator==(const It& i)const { return b == i.b; }
		constexpr bool operator!=(const It& i)const { return !(b == i.b); }
		constexpr T start()const { return a; }
		constexpr T count()const { return b; }
		constexpr T step()const { return c; }
	};
	constexpr Step(T b, T c, T s) : be(b, c, s) {}
	constexpr It begin()const { return be; }
	constexpr It end()const { return en; }
	constexpr T start()const { return be.start(); }
	constexpr T count()const { return be.count(); }
	constexpr T step()const { return be.step(); }
	constexpr T sum()const { return start() * count() + step() * (count() * (count() - 1) / 2); }
	operator vector<T>()const { return as_vector(); }
	vector<T> as_vector()const {
		vector<T> res; res.reserve(count()); each([&](T i) {res.push_back(i); }); return res;
	}
	template<class F>void each(const F& f)const { for (T i : *this)f(i); }
	template<class F>auto map(const F& f)const {
		vector<decay_t<result_of_t<F(T)>>> res; res.reserve(count());
		each([&](T i) {res.push_back(f(i)); }); return res;
	}
	template<class F>int count_if(const F& f)const {
		int res = 0; each([&](T i) {res += static_cast<bool>(f(i)); }); return res;
	}
	template<class F>vector<T> select(const F& f)const {
		vector<T> res; each([&](T i) {if (f(i))res.push_back(i); }); return res;
	}
	template<class F>auto max(const F& f)const {
		auto v = map(f); return *max_element(v.begin(), v.end());
	}
	template<class F>auto min(const F& f)const {
		auto v = map(f); return *min_element(v.begin(), v.end());
	}
	template<class F, class U = decay_t<result_of_t<F(T)>>>auto sum(const F& f)const {
		U res = 0; each([&](T i) {res += static_cast<U>(f(i)); }); return res;
	}
	using value_type = T;
	using iterator = It;
private:
	It be, en;
};
template<class T>inline constexpr auto step(T a) { return Step<T>(0, a, 1); }
template<class T>inline constexpr auto step(T a, T b) { return Step<T>(a, b - a, 1); }
template<class T>inline constexpr auto step(T a, T b, T c) { return Step<T>(a, a < b ? (b - a - 1) / c + 1 : 0, c); }

// --- functions --- //
inline namespace {
	template<class T>inline void Sort(T& a) { sort(all(a)); }
	template<class T>inline void RSort(T& a) { sort(rall(a)); }
	template<class T>inline T Sorted(T a) { Sort(a); return a; }
	template<class T>inline T RSorted(T a) { RSort(a); return a; }
	template<class T, class F>inline void Sort(T& a, const F& f) {
		sort(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T, class F>inline void RSort(T& a, const F& f) {
		sort(rall(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T>inline void Reverse(T& a) { reverse(all(a)); }
	template<class T>inline void Unique(T& a) { a.erase(unique(all(a)), a.end()); }
	template<class T>inline void Rotate(T& a, int left) { rotate(a.begin(), a.begin() + left, a.end()); }
	template<class T>inline T Reversed(T a) { Reverse(a); return a; }
	template<class T>inline T Uniqued(T a) { Unique(a); return a; }
	template<class T>inline T Rotated(T a, int left) { Rotate(a, left); return a; }
	template<class T>inline auto Max(const T& a) { return *max_element(all(a)); }
	template<class T>inline auto Min(const T& a) { return *min_element(all(a)); }
	template<class T>inline int MaxPos(const T& a) { return max_element(all(a)) - a.begin(); }
	template<class T>inline int MinPos(const T& a) { return min_element(all(a)) - a.begin(); }
	template<class T, class F>inline auto Max(const T& a, const F& f) {
		return *max_element(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T, class F>inline auto Min(const T& a, const F& f) {
		return *min_element(all(a), [&](const auto& x, const auto& y) {return f(x) < f(y); });
	}
	template<class T, class U>inline int Count(const T& a, const U& v) { return count(all(a), v); }
	template<class T, class F>inline int CountIf(const T& a, const F& f) { return count_if(all(a), f); }
	template<class T, class U>inline int Find(const T& a, const U& v) { return find(all(a), v) - a.begin(); }
	template<class T, class F>inline int FindIf(const T& a, const F& f) { return find_if(all(a), f) - a.begin(); }
	template<class T, class U = typename T::value_type>inline U Sum(const T& a) { return accumulate(all(a), U()); }
	template<class T, class F>inline auto Sum(const T& v, const F& f) {
		return accumulate(next(v.begin()), v.end(), f(v.front()), [&](auto a, auto b) {return a + f(b); });
	}
	template<class T, class U>inline int Lower(const T& a, const U& v) { return lower_bound(all(a), v) - a.begin(); }
	template<class T, class U>inline int Upper(const T& a, const U& v) { return upper_bound(all(a), v) - a.begin(); }
	template<class T, class F>inline void RemoveIf(T& a, const F& f) { a.erase(remove_if(all(a), f), a.end()); }
	template<class F>inline auto Vector(size_t size, const F& f) {
		vector<decay_t<result_of_t<F(size_t)>>> res(size); for (size_t i = 0; i < size; ++i)res[i] = f(i); return res;
	}
	template<class T>inline auto Grid(size_t h, size_t w, const T& v = T()) { return vector<vector<T>>(h, vector<T>(w, v)); }
	template<class T>inline auto Slice(const T& v, size_t i, size_t len) {
		return i < v.size() ? T(v.begin() + i, v.begin() + min(i + len, v.size())) : T();
	}
	template<class T, class F>inline auto Each(const T& v, const F& f) { for (auto& i : v)f(i); }
	template<class T, class F>inline auto Select(const T& v, const F& f) {
		T res; for (const auto& e : v)if (f(e))res.push_back(e); return res;
	}
	template<class T, class F>inline auto Map(const T& v, const F& f) {
		vector<decay_t<result_of_t<F(typename T::value_type)>>> res(v.size());
		size_t i = 0; for (const auto& e : v)res[i++] = f(e); return res;
	}
	template<class T, class F>inline auto MapIndex(const T& v, const F& f) {
		vector<decay_t<result_of_t<F(size_t, typename T::value_type)>>> res(v.size());
		size_t i = 0; for (auto it = v.begin(); it != v.end(); ++it, ++i)res[i] = f(i, *it); return res;
	}
	template<class T, class F>inline auto TrueIndex(const T& v, const F& f) {
		vector<size_t> res; for (size_t i = 0; i < v.size(); ++i)if (f(v[i]))res.push_back(i); return res;
	}
	inline string operator*(string s, size_t n) { string ret; for (size_t i = 0; i < n; ++i)ret += s; return ret; }
	template<class T>inline T Ceil(T n, T m) { return (n + m - 1) / m; }
	template<class T>inline T Ceil2(T n, T m) { return Ceil(n, m) * m; }
	template<class T>inline T Tri(T n) { return (n & 1) ? (n + 1) / 2 * n : n / 2 * (n + 1); }
	template<class T>inline T nC2(T n) { return (n & 1) ? (n - 1) / 2 * n : n / 2 * (n - 1); }
	template<class T>inline T Mid(const T& l, const T& r) { return l + (r - l) / 2; }
	inline int pop_count(int n) { return bitset<32>(n).count(); }
	inline int pop_count(ll n) { return bitset<64>(n).count(); }
	template<class T>inline bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; }
	template<class T>inline bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } return false; }
	template<class T>inline bool inRange(const T& v, const T& min, const T& max) { return min <= v && v < max; }
	template<class T = ll>inline T BIT(int b) { return T(1) << b; }
	template<class T>inline T Gcd(T n, T m) { return m ? Gcd(m, n % m) : n; }
	template<class T>inline T Lcm(T n, T m) { return n / Gcd(n, m) * m; }
	template<class T, class U = typename T::value_type>inline U Gcdv(const T& v) {
		return accumulate(next(v.begin()), v.end(), U(*v.begin()), Gcd<U>);
	}
	template<class T, class U = typename T::value_type>inline U Lcmv(const T& v) {
		return accumulate(next(v.begin()), v.end(), U(*v.begin()), Lcm<U>);
	}
	template<class T>inline T Pow(T a, T n) { T r = 1; while (n > 0) { if (n & 1)r *= a; a *= a; n /= 2; } return r; }
	template<class T>inline T Powmod(T a, T n, T m = MOD) {
		T r = 1; while (n > 0) { if (n & 1)r = r * a % m, n--; else a = a * a % m, n /= 2; }return r;
	}
}

// --- dump --- //
#if __has_include("dump.hpp")
#include "dump.hpp"
#else
#define dump(...) ((void)0)
#endif

// ---------------------------------------------------------------- //

int main() {
	INT(n, k);
	VL a = in[n];

	if (n == k) {
		out.exit(0);
	}

	auto dp = Grid<ll>(n, n, inf_ll);
	dp[0] = a;
	FOR(i, 1, n)FOR(j, i, n) {
		rep(k, j) {
			chmin(dp[i][j], dp[i - 1][k] + max(0ll, a[j] - a[k]));
		}
	}
	dump(dp);
	out(Min(dp[n - k - 1]));
}