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 <algorithm>
#include <bitset>
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <queue>
#include <set>
#include <tuple>
#include <vector>

using namespace std;

#define rep(i, n) for (int64_t i = 0; i < (int64_t)(n); i++)
#define irep(i, n) for (int64_t i = 0; i <= (int64_t)(n); i++)
#define rrep(i, n) for (int64_t i = (n)-1; i >= 0; i--)
#define rirep(i, n) for (int64_t i = n; i >= 0; i--)

#define chmax(a, b) (a) = max(a, b)
#define chmin(a, b) (a) = min(a, b)

template <int64_t MOD>
class Modint {
  using Self = Modint<MOD>;

  int64_t m_value;

 public:
  Modint() : m_value(0) {}
  Modint(int64_t value) : m_value((value % MOD + MOD) % MOD) {}
  Self pow(int64_t e) const {
    if (e == 0) {
      return (Self)1;
    } else if (e % 2 == 0) {
      return ((*this) * (*this)).pow(e / 2);
    } else {
      return (*this).pow(e - 1) * (*this);
    }
  }
  Self inv() const { return pow(MOD - 2); }
  Self& operator=(const Self& rh) {
    m_value = rh.m_value;
    return *this;
  }
  Self operator-() const { return Self(-m_value); }
  Self operator+(const Self& other) const {
    return Self(m_value + other.m_value);
  }
  Self operator-(const Self& other) const {
    return Self(m_value - other.m_value);
  }
  Self operator*(const Self& other) const {
    return Self(m_value * other.m_value);
  }
  Self operator/(const Self& other) const { return (*this) * other.inv(); }
  Self& operator+=(const Self& rh) { return (*this) = (*this) + rh; }
  Self& operator-=(const Self& rh) { return (*this) = (*this) - rh; }
  Self& operator*=(const Self& rh) { return (*this) = (*this) * rh; }
  Self& operator/=(const Self& rh) { return (*this) = (*this) / rh; }
  int64_t value() const { return m_value; }
};

int main() {
  int N, K;
  cin >> N >> K;

  vector<int> pos, neg;
  rep(i, N) {
    int a;
    cin >> a;
    if (a >= 0) {
      pos.push_back(a);
    } else {
      neg.push_back(-a);
    }
  }

  sort(pos.begin(), pos.end(), greater<int>());
  sort(neg.begin(), neg.end(), greater<int>());

  constexpr int64_t MOD = 1'000'000'007;
  using Mint = Modint<MOD>;

  Mint result = 1;
  if (N == K) {
    for (auto a : pos) {
      result *= a;
    }
    for (auto a : neg) {
      result *= -a;
    }
  } else if (N == neg.size()) {
    rep(i, K) { result *= -(K % 2 == 0 ? neg[i] : neg[N - 1 - i]); }
  } else {
    int M = min(K, (int)neg.size()) / 2 * 2;
    rep(i, M) { result *= neg[i]; }
    rep(i, K - M) { result *= pos[i]; }

    int j = M - 2;
    while (j >= 0 && K - j <= pos.size() &&
           (int64_t)pos[K - j - 2] * pos[K - j - 1] >
               (int64_t)neg[j] * neg[j + 1]) {
      result *= (int64_t)pos[K - j - 2] * pos[K - j - 1];
      result /= (int64_t)neg[j] * neg[j + 1];
      j -= 2;
    }
  }
  cout << result.value() << endl;

  return 0;
}