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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using Graph = vector<vector<int>>;
using WGraph = vector<vector<pair<int, ll>>>;

template<class T>inline bool chmax(T &a, const T &b) { if (b > a) { a = b; return true; } return false; }
template<class T>inline bool chmin(T &a, const T &b) { if (b < a) { a = b; return true; } return false; }

constexpr int dx[4] = {-1, 0, 0, 1}, dy[4] = {0, -1, 1, 0};
constexpr int INF = 1e9;
constexpr int MOD = 1e9 + 7;
constexpr long long LINF = 1e18;
constexpr double EPS = 1e-10;
constexpr double PI = M_PI;

template<int mod>
class ModInt {
    private:
        long long val;
    public:
        constexpr ModInt(const long long v = 0) : val(v%mod) { if (val < 0) val += mod; }
        constexpr ModInt(const ModInt &v) : val(v.val) {}
        constexpr ModInt &operator=(const long long v) { val = v; return *this; }
        constexpr ModInt &operator=(const ModInt &v) { if (this != &v) val = v.val; return *this; }
        constexpr ModInt operator+() const { return ModInt(val); }
        constexpr ModInt operator-() const { return ModInt(-val); }
        constexpr ModInt operator+(const ModInt &v) const { return ModInt(*this) += v; }
        constexpr ModInt operator-(const ModInt &v) const { return ModInt(*this) -= v; }
        constexpr ModInt operator*(const ModInt &v) const { return ModInt(*this) *= v; }
        constexpr ModInt operator/(const ModInt &v) const { return ModInt(*this) /= v; }
        constexpr ModInt &operator+=(const ModInt &v) { val += v.val; if (val >= mod) val -= mod; return *this; }
        constexpr ModInt &operator-=(const ModInt &v) { val -= v.val; if (val < 0) val += mod; return *this; }
        constexpr ModInt &operator*=(const ModInt &v) { val *= v.val; if (val >= mod) val %= mod; return *this; }
        constexpr ModInt &operator/=(const ModInt &v) { val *= v.inverse().val; if (val >= mod) val %= mod; return *this; }
        constexpr ModInt &operator++() { ++val; if (val >= mod) val -= mod; return *this; }
        constexpr ModInt &operator--() { --val; if (val < 0) val += mod; return *this; }
        constexpr ModInt operator++(int) { ModInt tmp(*this); operator++(); return tmp; }
        constexpr ModInt operator--(int) { ModInt tmp(*this); operator--(); return tmp; }
        constexpr bool operator==(const ModInt &v) const { return val == v.val; }
        constexpr bool operator!=(const ModInt &v) const { return !(*this == v); }
        friend std::istream &operator>>(std::istream &s, ModInt &v) { long long tmp; s >> tmp; v = ModInt(tmp); return s; }
        friend std::ostream &operator<<(std::ostream &s, const ModInt &v) { return s << v.val; }
        constexpr ModInt inverse() const {
            long long n = val, res = 1;
            while (n > 1) {
                res *= (mod - mod / n);
                res %= mod;
                n = mod % n;
            }
            return ModInt(res);
        }
        static constexpr ModInt modpow(ModInt v, long long n) {
            ModInt res(1);
            for ( ; n>0; n>>=1) {
                if (n & 1) res *= v;
                v *= v;
            }
            return res;
        }
};

using MInt = ModInt<MOD>;

void solve() {
    int N, K;
    cin >> N >> K;
    vector<int> plus, minus;
    for (int i=0; i<N; ++i) {
        int tmp;
        cin >> tmp;
        if (tmp >= 0) plus.push_back(tmp);
        else minus.push_back(-tmp);
    }

    int cntP = (int)plus.size(), cntM = (int)minus.size();
    sort(plus.rbegin(), plus.rend());
    sort(minus.rbegin(), minus.rend());
    vector<MInt> proP(cntP+1), proM(cntM+1);
    proP[0] = proM[0] = 1;
    for (int i=1; i<cntP+1; ++i) proP[i] = proP[i-1] * plus[i-1];
    for (int i=1; i<cntM+1; ++i) proM[i] = proM[i-1] * minus[i-1];
    if (cntP == 0) {
        if (K%2 == 0) {
            cout << proM[K] << '\n';
        } else {
            cout << - proM[N] / proM[N-K] << '\n';
        }
        return;
    }
    if (cntP == K-1 && cntM == 1) {
        cout << proP[K-1] * (-minus.back()) << '\n';
        return;
    }
    int curP = 0, curM = 0;
    curP = min(cntP, K);
    curM = K - curP;
    if (curM%2 == 1) --curP, ++curM;
    while (curP > 1 && curM + 1 < cntM) {
        if (minus[curM] * minus[curM+1] > plus[curP-1] * plus[curP-2]) {
            curM += 2;
            curP -= 2;
        } else {
            cout << proP[curP] * proM[curM] << '\n';
            return;
        }
    }
    cout << proP[curP] * proM[curM] << '\n';
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(20);

    solve();

    return 0;
}