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++ (GCC 9.2.1) (judge verdict: Accepted)

#include "bits/stdc++.h"
#include<random>
using namespace std;
typedef long long int lint;
typedef pair<lint, lint> plint;
typedef pair<double long, double long> pld;
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((lint)(x).size())
#define POW2(n) (1LL << (n))
#define FOR(i, begin, end) for(lint i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(lint i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template<class T>bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; }
template<class T>bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; }
template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2>& l, const pair<T1, T2>& r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2>& l, const pair<T1, T2>& r) { return make_pair(l.first - r.first, l.second - r.second); }
const lint MOD = 1e9 + 7, INF = 1e18;


template <std::int_fast64_t Modulus>
class modint
{
	using u64 = std::int_fast64_t;

public:
	u64 a;
	constexpr modint(const u64 x = 0) noexcept : a(x% Modulus) {}
	constexpr u64& value() noexcept { return a; }
	constexpr const u64& value() const noexcept { return a; }
	constexpr modint operator+(const modint rhs) const noexcept
	{
		return modint(*this) += rhs;
	}
	constexpr modint operator-(const modint rhs) const noexcept
	{
		return modint(*this) -= rhs;
	}
	constexpr modint operator*(const modint rhs) const noexcept
	{
		return modint(*this) *= rhs;
	}
	constexpr modint operator/(const modint rhs) const noexcept
	{
		return modint(*this) /= rhs;
	}
	constexpr modint& operator+=(const modint rhs) noexcept
	{
		a += rhs.a;
		if (a >= Modulus)
		{
			a -= Modulus;
		}
		return *this;
	}
	constexpr modint& operator-=(const modint rhs) noexcept
	{
		if (a < rhs.a)
		{
			a += Modulus;
		}
		a -= rhs.a;
		return *this;
	}
	constexpr modint& operator*=(const modint rhs) noexcept
	{
		a = a * rhs.a % Modulus;
		return *this;
	}
	constexpr modint& operator/=(modint rhs) noexcept
	{
		u64 exp = Modulus - 2;
		while (exp)
		{
			if (exp % 2)
			{
				*this *= rhs;
			}
			rhs *= rhs;
			exp /= 2;
		}
		return *this;
	}
};
typedef modint<MOD> ModInt;

ModInt mod_pow(ModInt x, ModInt n) {
	ModInt ret = 1;
	while (n.a > 0) {
		if (n.a & 1) (ret *= x);
		(x *= x);
		n.a >>= 1;
	}
	return ret;
}

ModInt func[200000];
void funcinit(int N)
{
	func[0] = 1;
	for (int i = 1; i <= N; i++)
	{
		func[i] = func[i - 1] * i;
	}
}
ModInt comb(ModInt n, ModInt r)
{
	if (n.a <= 0 || n.a < r.a)
	{
		return 0;
	}
	return func[n.a] / (func[r.a] * func[(n - r).a]);
}

lint N, K, _K, zero_cnt = 0;
lint arr[200000];
priority_queue<lint> pl;
priority_queue<lint> mn;
int main() {
	cin >> N >> K;
	_K = K;
	bool flag = true;
	REP(i, N) {
		cin >> arr[i];
		if (arr[i] >= 0) {
			pl.push(arr[i]);
			flag = false;
		}
		else mn.push(-arr[i]);
		if (arr[i] == 0) zero_cnt++;
	}
	
	ModInt ans = 1;

	if (flag && K%2 == 1) {
		sort(arr, arr + N, greater<lint>());
		REP(i, K) {
			ans *= arr[i];
		}
		cout << ans.a + MOD << endl;
		return 0;
	}

	while (K > 1) {
		lint plv = 1;
		if (pl.size() > 1) {
			plv *= pl.top();
			lint tmp = plv;
			pl.pop();
			plv *= pl.top();
			if (pl.size() > 1 && K %2 == 1) {
				lint tmp2 = pl.top();
				pl.pop();
				if (pl.top() == 0) {
					plv *= pl.top();
				}
				pl.push(tmp2);
			}
			pl.push(tmp);
		}

		lint mnv = 1;
		if (mn.size() > 1) {
			mnv *= mn.top();
			lint tmp = mnv;
			mn.pop();
			mnv *= mn.top();
			mn.push(tmp);
		}

		if ((plv >= mnv && ((pl.size() - zero_cnt > 2 && K % 2 == 1) || (pl.size() > 1 && K % 2 == 0))) || mn.size() < 2) {
			ans *= pl.top();
			pl.pop();
			K--;
		}
		else {
			ans *= mn.top();
			mn.pop();
			ans *= mn.top();
			mn.pop();
			K -= 2;
		}
	}
	if (pl.size() > 0 && K == 1) {
		ans *= pl.top();
	}
	else if (mn.size() > 0 && K == 1) {
		ans *= mn.top();
		ans = MOD - ans.a;
	}
	cout << ans.a << endl;
}