Problem:
Score : 500 points

Problem Statement

Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

1 \leq K \leq N \leq 2\times 10^5

|A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N K
A_1 \ldots A_N

Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Sample Input 1

4 2
1 2 -3 -4

Sample Output 1

12

The possible products of the two chosen elements are 2, -3, -4, -6, -8, and 12, so the maximum product is 12.

Sample Input 2

4 3
-1 -2 -3 -4

Sample Output 2

1000000001

The possible products of the three chosen elements are -24, -12, -8, and -6, so the maximum product is -6.

We print this value modulo (10^9+7), that is, 1000000001.

Sample Input 3

2 1
-1 1000000000

Sample Output 3

1000000000

The possible products of the one chosen element are -1 and 1000000000, so the maximum product is 1000000000.

Sample Input 4

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1

Sample Output 4

999983200

Be sure to print the product modulo (10^9+7).

Solution in C++ (Clang 10.0.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <deque>
#include <algorithm>
#include <numeric>
#include <string>
#include <cstring>
#include <list>
#include <unordered_set>
#include <tuple>
#include <cmath>
#include <limits>
#include <type_traits>
#include <iomanip>
#include <map>
#include <unordered_map>
#include <queue>
#include <stack>
#include <set>
#include <bitset>
#include <complex>
#include <regex>
#include <random>
using namespace std;

#define rep(i,n)	for(lint i = 0; i < n; i++)
#define repr(i,n)	for(lint i = n - 1; i >= 0; i--)
#define repi(i,ini,n)	for(lint i = ini; i < n; i++)
#define repir(i,ini,n)	for(lint i = n-1; i >= ini; i--)
#define repb(i,start,end)	for(lint i = start; i <= end; i++)
#define repbr(i,start,end)	for(lint i = end; i >= start; i--)

#define bit(n)				(1LL << (n))

#define all(v) v.begin(),v.end()
#define rall(v) v.rbegin(),v.rend()
#define rg(v, ini, end) v.begin() + ini, v.begin()+end
#define rrg(v, ini, end) v.rbegin() + ini, v.rbegin()+end

#define ret return 0;
#define chmax(a, b) a=mmax(a,b)
#define chmin(a, b) a=mmin(a,b)

namespace {

	using lint = long long;
	using ulint = unsigned long long;
	using ld = long double;
	struct xy
	{
		lint x, y;
		xy() :x(0), y(0) {}
		xy(lint _x, lint _y) : x(_x), y(_y) {}
		xy operator+(const xy& p) const
		{
			return xy(x + p.x, y + p.y);
		}
		bool operator<(xy p) const
		{
			if (y == p.y)
				return x < p.x;
			return y < p.y;
		}
	};
	struct xyd
	{
		ld x, y;
		xyd() :x(0), y(0) {}
		xyd(long double _x, long double _y) : x(_x), y(_y) {}
	};
	using vec = vector<lint>;
	using vecd = vector<ld>;
	using vecs = vector<string>;
	using vecp = vector<xy>;
	template<class T> using vect = vector<T>;
	class vec2 : public vector<vector<lint>>
	{
	public:
		vec2() {}
		vec2(lint n) : vector(n) {}
		vec2(lint h, lint w) : vector(h, vector<lint>(w)) {}
		vec2(lint h, lint w, lint v) : vector(h, vector<lint>(w, v)) {}
	};

	template<class T> using priq = priority_queue<T>;
	template<class T> using rpriq = priority_queue<T, vector<T>, greater<T>>;
	template<class Key, class Val> using hashmap = unordered_map<Key, Val>;
	template<class Key> using hashset = unordered_set<Key>;

	mt19937 mtrand((random_device())());

	const double pi = 3.141592653589793238462;
	const lint intmax = 9223372036854775807;
	const lint inf = 1100100100100100100LL;

	template<class T>
	constexpr auto msum(T arg0)
	{
		return arg0;
	}

	template<class T, class ...Types>
	constexpr auto msum(T arg0, Types ...args)
	{
		static_assert(sizeof...(args) > 0, "arg err");

		return arg0 + msum(args...);
	}

	template<class It>
	constexpr typename It::value_type mmax(It begin, It end)
	{
		return *max_element(begin, end);
	}

	template<class It>
	constexpr typename It::value_type mmin(It begin, It end)
	{
		return *min_element(begin, end);
	}

	template<class T>
	constexpr auto mmax(T arg)
	{
		return arg;
	}

	template<class T, class ...Types>
	constexpr auto mmax(T arg0, Types ...args)
	{
		using promote_t = decltype(msum(arg0, args...));

		return max(static_cast<promote_t>(arg0), static_cast<promote_t>(mmax(args...)));
	}

	template<class T>
	constexpr auto mmin(T arg)
	{
		return arg;
	}

	template<class T, class ...Types>
	constexpr auto mmin(T arg0, Types ...args)
	{
		using promote_t = decltype(msum(arg0, args...));

		return min(static_cast<promote_t>(arg0), static_cast<promote_t>(mmin(args...)));
	}

	template<class T>
	struct Mplus
	{
		T operator()(const T& a, const T& b)
		{
			return a + b;
		}

		const static T id = T(0);
	};

	template<
		class It,
		class T = typename It::value_type,
		class Monoid = Mplus<T>>
		T acc(It begin, It end, Monoid f = Mplus<T>())
	{
		return accumulate(begin, end, Monoid::id, f);
	}

	constexpr auto clamp(lint val, lint left, lint right)
	{
		return mmax(mmin(val, right), left);
	}

	constexpr lint div2(lint p, lint q)
	{
		return (p + q - 1) / q;
	}

#if(__cplusplus < 201703L)

	lint gcd(lint a, lint b) {
		while (1) {
			if (a < b) swap(a, b);
			if (!b) break;
			a %= b;
		}
		return a;
	}

	lint lcm(lint a, lint b)
	{
		return a / gcd(a, b) * b;
	}

#endif

	constexpr lint powInt(lint a, lint b)
	{
		if (b == 0)
		{
			return 1;
		}
		if (b == 1)
		{
			return a;
		}
		lint tmp = powInt(a, b / 2);
		return (b % 2 == 1 ? a * tmp * tmp : tmp * tmp);
	}

	template<class T>
	T sgn(T val)
	{
		if (val == T(0))
			return T(0);
		if (val < 0)
			return T(-1);
		if (val > 0)
			return T(1);
	}

	template<class T>
	constexpr auto modK_belowN(T k, T MOD, T n)
	{
		return (n + MOD - k - 1) / MOD;
	}

	template<class T, class Val>
	bool exist(const T& m, const Val& val)
	{
		return m.count(val) > 0;
	}

	template<class It, class T>
	bool exist(It begin, It end, const T& val)
	{
		return find(begin, end, val) != end;
	}

	template<class It, class Pr>
	bool exist_if(It begin, It end, Pr pred)
	{
		return find_if(begin, end, pred) != end;
	}

	template<class T>
	bool between(T val, T l, T r)
	{
		return (val >= l) && (val <= r);
	}

	lint extGCD(lint a, lint b, lint& x, lint& y) {
		if (b == 0) {
			x = 1;
			y = 0;
			return a;
		}
		lint d = extGCD(b, a % b, y, x);
		y -= a / b * x;
		return d;
	}

	template<class It>
	auto carr(It begin, It end) {
		vec c;
		c.push_back(1);
		auto before = *begin;
		for (auto it = begin + 1; it != end; it++) {
			if (before != *it) {
				c.push_back(0);
				before = *it;
			}
			c.back()++;
		}
		return c;
	}

	template<class T>
	struct nval {
		lint n;
		T val;
		nval() : n(0) {};
		nval(lint _n, T _val) : n(_n), val(_val) {};
	};

	template<class It>
	auto carr2(It begin, It end) {
		using T = nval<remove_reference_t<decltype(*begin)>>;

		vect<T> c;
		c.push_back(T(1, *begin));
		auto before = *begin;
		for (auto it = begin + 1; it != end; it++) {
			if (before != *it) {
				c.push_back(T(0, *it));
				before = *it;
			}
			c.back().n++;
		}
		return c;
	}

	template<class It, class ...T>
	void sort2(It begin, It end, T ...p)
	{
		using val_t = remove_reference_t<decltype(*begin)>;

		sort(begin, end, [p...](const val_t& a, const val_t& b) {
			bool neq[] = { (a.*p != b.*p)... };
			bool sg[] = { (a.*p < b.*p)... };

			rep(i, sizeof...(p)) {
				if (neq[i])
				{
					return sg[i];
				}
			}
			return false;
		});
	}

	template<class It, class It2>
	auto spacel(It i, It2 end)
	{
		if (i + 1 == end)
		{
			return '\n';
		}
		else
		{
			return ' ';
		}
	}

	bool match(string s, string r)
	{
		return regex_match(s, regex(r));
	}

	ostream& setp(ostream& ost)
	{
		cout << setprecision(60) << fixed;
		return ost;
	}

#ifdef _LOCAL
	auto& dbg = cout;
#else
	struct dummy_cout
	{
		template<class T>
		dummy_cout& operator<<(T&& op)
		{
			return *this;
		}

		using endl_t = basic_ostream<char, char_traits<char>>;

		dummy_cout& operator<<(endl_t& (*)(endl_t&))
		{
			return *this;
		}
	};

	dummy_cout dbg;
#endif

	const ulint mod = 1000000007;
	//const ulint mod = 998244353;
	const ld eps = 0.0000001;
};


struct mint
{
	lint n;
	mint()
	{
		n = 0;
	}
	mint(lint a)
	{
		n = a % mod;
	}
	mint& operator+=(mint a)
	{
		n += a.n;
		n %= mod;
		return *this;
	}
	mint& operator-=(mint a)
	{
		n += mod;
		n -= a.n;
		n %= mod;
		return *this;
	}
	mint& operator*=(mint a)
	{
		n *= a.n;
		n %= mod;
		return *this;
	}
	mint& operator%=(mint a)
	{
		n %= a.n;
		return *this;
	}
	mint& operator++()
	{
		n++;
		n %= mod;
		return *this;
	}
	mint& operator--()
	{
		n += mod;
		n--;
		n %= mod;
		return *this;
	}
};

mint operator+(mint a, mint b)
{
	a += b;
	return a;
}
mint operator-(mint a, mint b)
{
	a -= b;
	return a;
}
mint operator*(mint a, mint b)
{
	a *= b;
	return a;
}

int main()
{
	lint n, k;
	cin >> n >> k;
	vec a(n);
	rep(i, n)
		cin >> a[i];

	if (n == k)
	{
		mint ans = 1;
		rep(i, n)
		{
			ans *= abs(a[i]);
			if (a[i] < 0)
				ans = 0 - ans;
		}
		cout << ans.n << endl;
		ret;
	}

	if (k % 2 == 1 && mmax(all(a)) < 0)
	{
		sort(rall(a));
		mint ans = 1;
		rep(i, k)
		{
			ans *= abs(a[i]);
		}
		ans = 0 - ans;
		cout << ans.n << endl;
		ret;
	}

	lint buf = 1;
	vec b;
	rep(i, n)
	{
		if (a[i] < 0)
		{
			if (buf == 1)
				buf = a[i];
			else
			{
				b.push_back(-a[i] * buf);
				buf = 1;
			}
		}
		else
		{
			b.push_back(a[i]);
		}
	}

	sort(rall(b), [](lint a, lint b)
		{
			return abs(a) < abs(b);
		});

	lint i = 0;
	mint ans = 1;

	while (k > 0)
	{
		if (k == 1 && b[i] < 0)
		{
			i++;
			continue;
		}
		ans *= abs(b[i]);
		if (b[i] < 0)
			k--;
		k--;
		i++;
	}

	cout << ans.n << endl;

	return 0;
}