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)

// {{{ by unolight
#include <bits/stdc++.h>
#include <unistd.h>
#pragma GCC diagnostic ignored "-Wunused-result"
#pragma GCC diagnostic ignored "-Wunused-function"
#define SZ(x) ((int)(x).size())
#define ALL(x) begin(x),end(x)
#define RALL(x) rbegin(x),rend(x)
#define REP(i,n) for ( int i=0; i<int(n); i++ )
#define REP1(i,a,b) for ( int i=(a); i<=int(b); i++ )
#define MP make_pair
#define PB push_back
using namespace std;
typedef int64_t LL;
typedef pair<int,int> PII;
typedef vector<int> VI;

namespace { namespace unolight {
// Read Input
template<class T> void _R( T &x ) { cin>>x; }
void _R( int &x ) { scanf("%d",&x); }
void _R( int64_t &x ) { scanf("%" PRId64,&x); }
void _R( double &x ) { scanf("%lf",&x); }
void _R( char &x ) { scanf(" %c",&x); }
void _R( char *x ) { scanf("%s",x); }
void R() {}
template<class T, class... U> void R( T& head, U&... tail ) { _R(head); R(tail...); }
// Write Output
template<class T> void _W( const T &x ) { cout<<x; }
void _W( const int &x ) { printf("%d",x); }
void _W( const int64_t &x ) { printf("%" PRId64,x); }
void _W( const double &x ) { printf("%.16f\n",x); }
void _W( const char &x ) { putchar(x); }
void _W( const char *x ) { printf("%s",x); }
template<class T> void _W( const vector<T> &x ) { for (auto i = x.begin(); i != x.end(); _W(*i++)) if (i != x.cbegin()) putchar(' '); }
void W() {}
template<class T, class... U> void W( const T& head, const U&... tail ) { _W(head); putchar(sizeof...(tail)?' ':'\n'); W(tail...); }

#ifdef UNOLIGHT
#include "dump.hpp"
#else
#define dump(...)
#endif

template<class T> inline bool chmax( T &a, const T &b ) { return b>a ? a=b,true : false; }
template<class T> inline bool chmin( T &a, const T &b ) { return b<a ? a=b,true : false; }
template<class T> using MaxHeap = priority_queue<T>;
template<class T> using MinHeap = priority_queue<T, vector<T>, greater<T>>;
template<class T, class F=less<T>> void sort_uniq( vector<T> &v, F f=F() ) {
    sort(begin(v),end(v),f);
    v.resize(unique(begin(v),end(v))-begin(v));
}
// }}}

// {{{ ModInt
template<int _MOD>
struct ModInt {
	static const auto MOD = _MOD;
	template<class T> using integral_only = typename enable_if<is_integral<T>::value>::type;

    int x;   
	constexpr ModInt() : x() {}

	template<class T, integral_only<T>* = nullptr>
    ModInt(T _x=0) {
		x = _x % MOD;
		if(x<0) x+=MOD;
	}
    ModInt operator-() const { return {x == 0? 0 : MOD-x}; }
    ModInt& operator+=(const ModInt a) {
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    ModInt& operator-=(const ModInt a) {
        if ((x += MOD-a.x) >= MOD) x -= MOD;
        return *this;
    }
    ModInt& operator*=(const ModInt a) {
        x = (long long)x * a.x % MOD;
        return *this;
    }
    ModInt& operator/=(const ModInt a) {
        return (*this) *= a.inv();
    }

    ModInt operator+(const ModInt a) const { return ModInt(*this) += a; }
    ModInt operator-(const ModInt a) const { return ModInt(*this) -= a; }
    ModInt operator*(const ModInt a) const { return ModInt(*this) *= a; }
    ModInt operator/(const ModInt a) const { return ModInt(*this) /= a; }
    ModInt inv() const {
	    // for prime MOD
        return pow(MOD-2);
    }
	ModInt inv2() const {
		// work for non-prime MOD if gcd(x,MOD) = 1
		int a = x, b = MOD, u = 1, v = 0;
		while(b != 0) {
			int t = a / b;
			a -= t * b;
			u -= t * v;
			swap(a, b);
			swap(u, v);
		}
		return u;
	}
	template<class T, integral_only<T>* = nullptr>
    ModInt pow(T t) const {
		ModInt r = 1, p = *this;
		while(t) {
			if(t & 1) r *= p;
			p *= p;
			t >>= 1;
		}
        return r;
    }

    bool operator==(ModInt rhs) const { return x == rhs.x; }
    bool operator!=(ModInt rhs) const { return x != rhs.x; }
    bool operator<(ModInt rhs) const { return x < rhs.x; }
    bool operator<=(ModInt rhs) const { return x <= rhs.x; }
    bool operator>(ModInt rhs) const { return x > rhs.x; }
    bool operator>=(ModInt rhs) const { return x >= rhs.x; }

    friend string to_string(ModInt i) { return to_string(i.x); }
    friend istream& operator>>(istream&i,ModInt&a) { return i>>a.x; }
    friend ostream& operator<<(ostream&o,const ModInt&a) { return o<<a.x; }
};

const int MOD=1000000007;
using mint=ModInt<MOD>;
// }}}

void main() {
    int n, k;
    vector<LL> pos;
    vector<LL> neg;
    R(n,k);
    bool z=false;
    REP(i,n) {
        LL a;
        R(a);
        if ( a==0 ) z=true;
        else if ( a>0 ) pos.push_back(a);
        else neg.push_back(-a);
    }
    if ( SZ(pos)+SZ(neg)<k ) {
        W(0);
        return;
    }

    if ( SZ(pos)==0 ) {
        if ( k%2 && z ) {
            W(0);
            return;
        } 
        LL ans=1;
        REP(i,k) ans=ans*-1*neg[i]%MOD;
        W((ans+MOD)%MOD);
        return;
    }

    sort(ALL(pos));
    sort(ALL(neg));
    vector<LL> P,N;
    while ( SZ(P)+SZ(N)<k ) {
        if ( SZ(pos) && SZ(neg) ) {
            if ( pos.back()>=neg.back() ) {
                P.push_back(pos.back());
                pos.pop_back();
            } else {
                N.push_back(neg.back());
                neg.pop_back();      
            }
        } else if ( SZ(pos) ) {
            P.push_back(pos.back());
            pos.pop_back();
        } else if ( SZ(neg) ) {
            N.push_back(neg.back());
            neg.pop_back();      
        } else {
            W(0);
            return;
        }
    }

    if ( SZ(N)%2 ) {
        // 1. remove 1 positive, add 1 negative
        // 2. remove 1 negative, add 1 positive
        if ( SZ(N) && SZ(pos) && SZ(P) && SZ(neg) ) {
            if ( pos.back()*P.back() >= neg.back()*N.back() ) {
                N.pop_back();
                P.push_back(pos.back());
            } else {
                P.pop_back();
                N.push_back(neg.back());
            }
        } else if ( SZ(N) && SZ(pos) ) {
            N.pop_back();
            P.push_back(pos.back());
        } else if ( SZ(P) && SZ(neg) ) {
            P.pop_back();
            N.push_back(neg.back());
        }
    }
    mint ans=1;
    for ( LL i:P ) ans*=i;
    for ( LL i:N ) ans*=i;
    W(ans);
}

}} // {{{ main
int main() { unolight::main(); return 0; }
// }}}