Problem:
Score : 300 points

Problem Statement

There are N candles placed on a number line.
The i-th candle from the left is placed on coordinate x_i.
Here, x_1 < x_2 < ... < x_N holds.

Initially, no candles are burning.
Snuke decides to light K of the N candles.

Now, he is at coordinate 0.
He can move left and right along the line with speed 1.
He can also light a candle when he is at the same position as the candle, in negligible time.

Find the minimum time required to light K candles.

Constraints

1 \leq N \leq 10^5

1 \leq K \leq N

x_i is an integer.

|x_i| \leq 10^8

x_1 < x_2 < ... < x_N

Input

Input is given from Standard Input in the following format:

N K
x_1 x_2 ... x_N

Output

Print the minimum time required to light K candles.

Sample Input 1

5 3
-30 -10 10 20 50

Sample Output 1

40

He should move and light candles as follows:

Move from coordinate 0 to -10.

Light the second candle from the left.

Move from coordinate -10 to 10.

Light the third candle from the left.

Move from coordinate 10 to 20.

Light the fourth candle from the left.

Sample Input 2

3 2
10 20 30

Sample Output 2

20

Sample Input 3

1 1
0

Sample Output 3

0

There may be a candle placed at coordinate 0.

Sample Input 4

8 5
-9 -7 -4 -3 1 2 3 4

Sample Output 4

10

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<vector>
#include<map>
#include<set>
#include<algorithm>
#include<numeric>
#include<limits>
#include<bitset>
#include<functional>
#include<type_traits>
#include<queue>
#include<stack>
#include<array>
#include<random>
#include<utility>

#include<boost/multi_array.hpp>
#include<boost/variant.hpp>
#include<boost/optional.hpp>
#include<boost/optional/optional_io.hpp>
#include<boost/range/irange.hpp>
#include<boost/range/algorithm.hpp>
#include<boost/range/adaptors.hpp>
#include<boost/range/size.hpp>
#include<boost/range/has_range_iterator.hpp>
#include<boost/multiprecision/cpp_int.hpp>

#ifdef _MSC_FULL_VER
#include"randomizer.hpp"
#endif

#include<cstdlib>
#include<ctime>

#define DEFINE_STRUCT2(arg0,arg1,stc)\
auto const& arg0=std::get<0>(stc);\
auto const& arg1=std::get<1>(stc)

#define DEFINE_STRUCT3(arg0,arg1,arg2,stc)\
DEFINE_STRUCT2(arg0,arg1,stc);\
auto const& arg2=std::get<2>(stc)

namespace lib
{
	using namespace boost::range;
	template<class T>constexpr T pow(T base, std::size_t p)
	{
		return
			p == 0 ? T(1) :
			p == 1 ? base :
			p == 2 ? base * base :
			p % 2 == 0 ?
			pow(pow(base, p / 2), 2) :
			pow(pow(base, p / 2), 2)*base;
	}

	template<class T>constexpr T gcd(T a, T b)
	{
		return a > b ? gcd(b, a) : a == T() ? b : gcd(b%a, a);
	}

	constexpr int intlog2(std::int64_t x)
	{
		std::int64_t j = 2;
		for (auto i = 0; i < 63; ++i)
		{
			if (j > x)
			{
				return int(i);
			}
			j <<= 1;
		}
		return 63;
	}

	template<class T>using p_queue = std::priority_queue<T, std::vector<T>, std::greater<>>;

	struct union_find_light
	{
		std::vector<int> upper;
		union_find_light(std::size_t size):upper(size, -1) {}

		int group(int index)
		{
			if (upper[index] == -1)
			{
				return index;
			}
			else
			{
				return upper[index] = group(upper[index]);
			}
		}

		bool merge(int x, int y)
		{
			auto gx = group(x);
			auto gy = group(y);
			if (gx != gy)
			{
				upper[gx] = gy;
				return true;
			}
			return false;
		}

		auto get()
		{
			std::map<int, std::set<int>> ret;
			for (int i = 0; i < upper.size(); ++i)
			{
				ret[group(i)].emplace(i);
			}
			return ret;
		}

		auto tops()
		{
			std::set<int> ret;
			for (int i = 0; i < upper.size(); ++i)
			{
				ret.emplace(group(i));
			}
			return ret;
		}

		bool is_same_group(int x, int y)
		{
			return group(x) == group(y);
		}
	};

	template<class Selector>auto make_compare(Selector selector)
	{
		return [=](auto const& lhs, auto const& rhs) {return selector(lhs) < selector(rhs); };
	}

	template<class Iterator>auto make_range(Iterator first, Iterator last)
	{
		struct return_type
		{
			Iterator first;
			Iterator last;
			auto begin()const
			{
				return first;
			}
			auto end()const
			{
				return last;
			}
		};
		return return_type{ first, last };
	}

	template<class T>auto factorial_array(std::size_t max)
	{
		std::vector<T> ret(max + 1);
		ret[0] = 1;
		for (auto i : boost::irange<std::size_t>(1, max + 1))
		{
			ret[i] = ret[i - 1] * T(i);
		}
		return ret;
	}

	auto const first = [](auto p) {return p.first; };
	auto const second = [](auto p) {return p.second; };

	auto maxf = [](auto a, auto b) {return std::max(a, b); };
	auto minf = [](auto a, auto b) {return std::min(a, b); };

	template<class T>using dual_array = boost::multi_array<T, 2>;
	template<class T>using optional_dual_array = boost::multi_array<boost::optional<T>, 2>;
	template<class T>constexpr T min_value = std::numeric_limits<T>::min();
	template<class T>constexpr T max_value = std::numeric_limits<T>::max();
}

namespace out
{
	namespace detail
	{
		template<class>struct void_out
		{
			typedef void type;
		};
		
		template<class T>auto write(std::ostream& ost, T const& val)
			->typename void_out<decltype(ost << val)>::type
		{
			ost << val;
		}
		template<class T, class... Ts>void write(std::ostream& ost, T const& val, Ts const&... nexts)
		{
			write(ost, val);
			ost << " ";
			write(ost, nexts...);
		}
		template<class T, std::size_t... Is>void write_tuple(std::ostream& ost, T const& tuple, std::index_sequence<Is...>)
		{
			write(ost, std::get<Is>(tuple)...);
		}
		template<class... Ts>void write(std::ostream& ost, std::tuple<Ts...>const& tuple)
		{
			write_tuple(ost, tuple, std::make_index_sequence<sizeof...(Ts)>());
		}
		template<class T, class U>void write(std::ostream& ost, std::pair<T, U>const& pair)
		{
			write(ost, pair.first, pair.second);
		}
		template<class T>void write(std::ostream& ost, boost::optional<T>const& opt)
		{
			if (opt)
			{
				write(ost, *opt);
			}
			else
			{
				write(ost, "--");
			}
		}
		template<class T>auto write(std::ostream& ost, T const& vec)
			->std::enable_if_t<std::is_same<decltype(std::begin(vec)), decltype(std::end(vec))>::value &&
			!std::is_same<T, std::string>::value>
		{
			for (auto const& v : vec)
			{
				write(ost, v);
				ost << " ";
			}
		}
	}
	void write_line()
	{
		std::cout << std::endl;
	}
	template<class...Ts>void write_line(Ts const&... args)
	{
		detail::write(std::cout, args...);
		write_line();
	}
	template<class Range>void write_range(Range const& rng)
	{
		for (auto const& v : rng)
		{
			write_line(v);
		}
	}
}

namespace in
{
	template<class T>auto read(T& v)
		->typename out::detail::void_out<decltype(std::cin >> v)>::type
	{
		std::cin >> v;
	}
	template<class T, class U>void read(std::pair<T, U>& p)
	{
		read(p.first);
		read(p.second);
	}
	template<class T>std::vector<T> read_vector(std::size_t N)
	{
		std::vector<T> vec(N);
		for (auto& v : vec)
		{
			read(v);
		}
		return vec;
	}
}

namespace adaptor = boost::adaptors;

void Main()
{
	int N, K;
	std::cin >> N >> K;
	std::vector<std::int64_t>minus = { 0 }, plus = { 0 };
	for (int i : boost::irange(0, N))
	{
		std::int64_t v;
		std::cin >> v;
		if (v < 0)
		{
			minus.emplace_back(-v);
		}
		else
		{
			plus.emplace_back(v);
		}
	}
	lib::sort(minus);
	int m = minus.size() - 1;
	int p = plus.size() - 1;
	std::int64_t min = lib::max_value<std::int64_t>;
	for (int i = std::max(0, K - p); i <= std::min(K, m); ++i)
	{
		auto a = plus[K - i];
		auto b = minus[i];
		min = std::min(min, a + b + std::min(a, b));
	}
	out::write_line(min);
}

int main()
{
	std::cin.tie(nullptr);
	std::cin.sync_with_stdio(false);
	std::cout << std::fixed << std::setprecision(15);
	Main();
}