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>

using namespace std;
 
#define debug(s) cerr << #s << " = " << s << '\n'
#define all(v) (v).begin(), (v).end()
#define mem(a,val) memset(a, val, sizeof a)
 
#define ff first
#define ss second
typedef long long ll;

const int N = 200010;
const int mod = 1e9 + 7;
int n, k;
ll arr[N];

bool cmp(ll A, ll B) {
  return abs(A) > abs(B);
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> k;
  bool noneg = false;
  for (int i = 1; i <= n; ++i) {
    cin >> arr[i];
    if (arr[i] >= 0) noneg = true;
  }
  sort(arr + 1, arr + 1 + n, cmp);
  if (n == k) {
    ll ans = 1LL;
    for (int i = 1; i <= n; ++i) ans = (ans * arr[i]) % mod;
    if (ans < 0) ans += mod;
    cout << ans << '\n';
    return 0;
  }
  if (!noneg) {
    if (k & 1) {
      ll ans = 1LL;
      reverse(arr + 1, arr + 1 + n);
      for (int i = 1; i <= k; ++i) ans = (ans * arr[i]) % mod;
      if (ans < 0) ans += mod;
      cout << ans << '\n';
      return 0;
    } else {
      ll ans = 1LL;
      for (int i = 1; i <= k; ++i) ans = (ans * arr[i]) % mod;
      if (ans < 0) ans += mod;
      cout << ans << '\n';
      return 0;
    }
  }
  int lstneg = -1, lstnon = -1;
  int cntn = 0;
  for (int i = 1; i <= k; ++i) {
    if (arr[i] < 0) {
      lstneg = i;
      cntn++;
    }
    else lstnon = i;
  }
  if (!(cntn & 1)) {
    ll ans = 1LL;
    for (int i = 1; i <= k; ++i) ans = (ans * arr[i]) % mod;
    cout << ans << '\n';
    return 0;
  }
  int nxtneg = -1, nxtnon = -1;
  for (int i = k + 1; i <= n; ++i) {
    if (arr[i] < 0 && nxtneg == -1) {
      nxtneg = i;
    } else if (arr[i] >= 0 && nxtnon == -1) {
      nxtnon = i;
    }
  }
  if (lstnon == -1) {
    swap(arr[lstneg], arr[nxtnon]);
  } else if (nxtneg == -1) {
    swap(arr[lstneg], arr[nxtnon]);
  } else if (nxtnon == -1) {
    swap(arr[lstnon], arr[nxtneg]);
  } else {
    ll va = arr[lstnon]*arr[nxtnon];
    ll vb = arr[lstneg]*arr[nxtneg];
    if (va > vb) swap(arr[lstneg], arr[nxtnon]);
    else swap(arr[lstnon], arr[nxtneg]);
  }
  ll ans = 1LL;
  for (int i = 1; i <= k; ++i) ans = (ans * arr[i]) % mod;
  if (ans < 0) ans += mod;
  cout << ans << '\n';
}