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>
#include <unistd.h>
#include <time.h>
#include <sys/time.h>

using namespace std;

///////////////////////////////////////////////////////////////////////////////

#define DEBUG 0

#define pb push_back
#define V vector
#define M unordered_map
#define S static
#define PI  (3.1415926535)

#define rep(i,n) for(ll i=0LL; i<n; ++i)
#define srep(i,s,n) for(ll i=s; i<n; ++i)
#define rrep(i,n) for(ll i=n-1LL; i>=0LL; --i)
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define CIN(x) do { \
        assert(!cin.eof()); \
        cin >> x; \
        assert(!cin.fail()); \
} while(0);
#if DEBUG
#define debug_print(...) _debug_print(__VA_ARGS__)
#define debug_printf(...) printf(__VA_ARGS__)
#define debug_print_time _debug_print_time
#else // DEBUG
#define debug_print(...)
#define debug_printf(...)
#define debug_print_time
#endif // DEBUG

typedef long long ll;
typedef unsigned long long ull;
typedef tuple<ll, ll> t2;
typedef tuple<ll, ll, ll> t3;
typedef tuple<ll, ll, ll, ll> t4;
typedef tuple<ll, ll, ll, ll, ll> t5;
template <typename T>
using priority_queue_incr = priority_queue<T, V<T>, greater<T> >;

///////////////////////////////////////////////////////////////////////////////

template <typename TT, typename T>
T get_m(M<TT, T> &m, TT k, T default_value)
{
    if (m.find(k) == m.end()) return m[k] = default_value;
    return m[k];
}

template <typename TT, typename T>
void incr_m(M<TT, T> &m, TT k)
{
    if (m.find(k) == m.end()) m[k] = 0;
    m[k]++;
}

void llin(ll &a)
{
    CIN(a);
}

void llinl1(V<ll> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a;
        CIN(a);
        v.push_back(a);
    }
}

void llinl2(V<t2> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b;
        CIN(a >> b);
        v.push_back(t2(a, b));
    }
}

void llinl3(V<t3> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c;
        CIN(a >> b >> c);
        v.push_back(t3(a, b, c));
    }
}

void llinl4(V<t4> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c, d;
        CIN(a >> b >> c >> d);
        v.push_back(t4(a, b, c, d));
    }
}

void llina(V<ll> &v, ll count)
{
    llinl1(v, count);
}

template <typename T>
void sort(V<T> &v)
{
    sort(v.begin(), v.end());
}

template <typename T>
void sort_reverse(V<T> &v)
{
    sort(v.begin(), v.end(), greater<T>());
}

template <typename T>
void _debug_print(T x)
{
    cout << x << endl;
}

void _debug_print(const t2 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    cout << "-- " << x1 << " -- " << x2 << endl;
}

void _debug_print(const t3 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    cout << "-- " << x1 << " -- " << x2 << " -- " << x3 << endl;
}

void _debug_print(const t4 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    ll x4 = get<3>(x);
    cout << "-- " << x1 << " -- " << x2
         << " -- " << x3 << " -- " << x4 << endl;
}

template <typename T>
void _debug_print(T xarray[], ll n)
{
    rep (i, n) _debug_print(xarray[i]);
}

template <typename T>
void _debug_print(const V<T> &xlist)
{
    for (auto x : xlist) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename T>
void _debug_print(const set<T> &xset)
{
    for (auto x : xset) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename TT, typename T>
void _debug_print(const M<TT, T> &xlist)
{
    for (auto x : xlist) {
        TT k = x.first;
        T v = x.second;
        cout << "====" << endl;
        cout << "K=";
        _debug_print(k);
        cout << "V=";
        _debug_print(v);
    }
}

void _debug_print_time(const char *prefix)
{
    struct timeval tv;
    gettimeofday(&tv, NULL);
    struct tm *tm = localtime(&tv.tv_sec);
    printf("-- %s %02d:%02d:%02d.%06ld\n",
           prefix, tm->tm_hour, tm->tm_min, tm->tm_sec, tv.tv_usec);
}




#define MOD   (1000000007LL)
// #define MOD   (998244353LL)

ll mod_mlt(ll x, ll y, ll mod)
{
    ll ret = 0LL;
    x %= mod;

    while (y) {
        if (y & 1LL) {
            ret += x;
            ret %= mod;
        }
        y >>= 1;
        x <<= 1;
        x %= mod;
    }

    return ret;
}

// O(log(exp))
ll mod_pow(ll base, ll exp, ll mod)
{
    ll ret = 1LL;

    for ( ; exp; ) {
        if (exp & 1LL) {
            ret *= base;
            ret %= mod;
        }
        base = (base * base) % mod;
        exp >>= 1;
    }

    return ret;
}

// O(log(mod))
ll mod_inv(ll x, ll mod)
{
    // available only when mod is prime
    return mod_pow(x, mod - 2LL, mod);
}

ull mod_combination(ll x, ll y, ll mod)
{
    if (y > x / 2LL) y = x - y;

    ll ret = 1;

    for (ll i = 0LL; i < y; ++i) {
        ret = (ret * x--) % mod;
        ret = (ret * mod_inv(i + 1LL, mod)) % mod;
    }

    return ret;
}

void make_perms(ll perms[], ll perm_invs[], ll size, ll mod)
{
    perms[0] = 1LL;
    srep (i, 1, size) {
        perms[i] = perms[i-1] * i;
        perms[i] %= mod;
    }

    perm_invs[size-1] = mod_inv(perms[size-1], mod);
    rrep (i, size-1) {
        perm_invs[i] = perm_invs[i+1LL] * (i+1LL);
        perm_invs[i] %= mod;
    }
}




///////////////////////////////////////////////////////////////////////////////

void _main();
int main()
{
    cout << setprecision(12);
#if !DEBUG
    ios::sync_with_stdio(false);
    cin.tie(0);
#endif

    _main();
    return 0;
}

ll cmp(ll cand1_add, ll cand1_rem, ll cand2_add, ll cand2_rem)
{
    if (cand1_add * cand2_rem < cand1_rem * cand2_add) return 1;
    if (cand1_add * cand2_rem > cand1_rem * cand2_add) return -1;
    return 0;
}

void _main()
{
    ll n; llin(n);
    ll k; llin(k);
    V<ll> alist; llina(alist, n);

    V<ll> negs;
    V<ll> poss;
    ll zerocnt = 0;
    for (auto a : alist) {
        if (a > 0) poss.pb(a);
        if (a < 0) negs.pb(-a);
        if (a == 0) zerocnt++;
    }

    if (negs.size() + poss.size() < k) {
        debug_printf("----- ans 1\n");
        cout << 0 << endl;
        return;
    }

    if (poss.size() == 0 && zerocnt == 0) {
        ll xans = 1;
        if (k & 1LL) {
            sort(negs);
            rep (i, k) {
                xans *= negs[i];
                xans %= MOD;
            }
            debug_printf("xxx = %lld\n", xans);
            xans = -xans;
            if (xans < 0) xans += MOD;
        }
        else {
            sort_reverse(negs);
            rep (i, k) {
                xans *= negs[i];
                xans %= MOD;
            }
        }
        debug_printf("----- xans\n");
        cout << xans << endl;
        return;
    }

    priority_queue<t2> q;
    for (auto a : poss) q.push(t2(a, 1));
    for (auto a : negs) q.push(t2(a, -1));

    ll poscnt = 0;
    ll negcnt = 0;
    ll lastpos = -1;
    ll lastneg = -1;
    ll ans = 1;
    rep (xx, k) {
        auto item = q.top(); q.pop();
        ll a = get<0>(item);
        ll type = get<1>(item);
        ans *= a;
        ans %= MOD;
        if (type == 1) {
            poscnt++;
            lastpos = a;
        }
        else {
            negcnt++;
            lastneg = a;
        }
    }

    if (!(negcnt & 1LL)) {
        debug_printf("----- ans 2\n");
        cout << ans << endl;
        return;
    }
    if (negcnt == negs.size()) {
        ans *= mod_inv(lastneg, MOD);
        ans %= MOD;
        auto item = q.top(); q.pop();
        assert(get<1>(item) == 1);
        ans *= get<0>(item);
        ans %= MOD;
        debug_printf("----- ans 3\n");
        cout << ans << endl;
        return;
    }
    if (poscnt == poss.size()) {
        if (poscnt == 0) {
            if (zerocnt) {
                debug_printf("----- ans 4.1\n");
                cout << 0 << endl;
            }
            else {
                debug_printf("----- ans 4.2\n");
                ans = -ans;
                while (ans < 0) ans += MOD;
                cout << ans << endl;
            }
            return;
        }
        if (negcnt == negs.size()) {
            debug_printf("----- ans 5\n");
            cout << 0 << endl;
            return;
        }
        ans *= mod_inv(lastpos, MOD);
        ans %= MOD;
        auto item = q.top(); q.pop();
        assert(get<1>(item) == -1);
        ans *= get<0>(item);
        ans %= MOD;
        debug_printf("----- ans 6\n");
        cout << ans << endl;
        return;
    }
    if (poscnt == 0) {
        ans *= mod_inv(lastneg, MOD);
        ans %= MOD;
        ll a = -1;
        while (q.size()) {
            auto item = q.top(); q.pop();
            a = get<0>(item);
            ll type = get<1>(item);
            if (type == 1) break;
        }
        ans *= a;
        ans %= MOD;
        debug_printf("----- ans 7\n");
        cout << ans << endl;
        return;
    }

    ll cand1_rem = lastneg;
    ll cand1_add = -1;
    ll cand2_rem = lastpos;
    ll cand2_add = -1;
    while (q.size()) {
        auto item = q.top(); q.pop();
        ll a = get<0>(item);
        ll type = get<1>(item);
        if (cand1_add < 0 && type == 1) cand1_add = a;
        if (cand2_add < 0 && type == -1) cand2_add = a;
        if (cand1_add >= 0 && cand2_add >= 0) break;
    }

    // if (cand1_add * cand2_rem < cand1_rem * cand2_add) return 1;
    if (cmp(cand1_add, cand1_rem, cand2_add, cand2_rem) > 0) {
        ans *= mod_inv(cand2_rem, MOD);
        ans %= MOD;
        ans *= cand2_add;
        ans %= MOD;
    }
    else {
        ans *= mod_inv(cand1_rem, MOD);
        ans %= MOD;
        ans *= cand1_add;
        ans %= MOD;
    }

    debug_printf("----- ans 8\n");
    cout << ans << endl;
}

///////////////////////////////////////////////////////////////////////////////