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;
const int MAXN = 2e5 + 5;
const int MOD = 1e9+7;
bool cmp(long long a,long long b)
{
    return abs(a) > abs(b);
}
int a[MAXN];
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);cout.tie(0);

    int n,k,temp,cnt = 0,flag = 0;
    cin >> n >> k;
    for(int i = 0; i < n; i++){
        cin >> a[i];
        if(a[i] < 0)
            cnt++;
        else if(a[i] == 0)
            flag = 1;
    }
    sort(a,a+n,cmp);
    long long ans = 1;
//    for(int i = 0; i < n; i++)
//        cout << a[i] << ' ';
    if(cnt == n)
    {
        if(k%2==0)
            for(int i = 0; i < k; i++)
                ans = ans * a[i] % MOD;
        else
            for(int i = n-1; i > n-1-k; i--)
            {
                ans = ans * a[i] % MOD;
//                cout << i << endl;
            }
    }else if(cnt == 0)
    {
        for(int i = 0; i < k; i++)
            ans = ans * a[i] % MOD;
    }else{
        for(int i = 0; i < k; i++)
            ans = ans * a[i] % MOD;
        if(ans < 0)
        {
            int pos1, pos2;
            long long ans1 = 1, ans2 = 1;
            for(int i = k-1; i >= 0; i--)
            {
                if(a[i] < 0)
                {
                    pos1 = i;
                    break;
                }
            }
            for(int i = k; i < n; i++)
            {
                if(a[i] > 0)
                {
                    pos2 = i;
                    break;
                }
            }
            swap(a[pos1],a[pos2]);
            for(int i = 0; i < k; i++)
                ans1 = ans * a[i] % MOD;
            swap(a[pos1],a[pos2]);
            for(int i = k-1; i >= 0; i--)
            {
                if(a[i] > 0)
                {
                    pos1 = i;
                    break;
                }
            }
            for(int i = k; i < n; i++)
            {
                if(a[i] < 0)
                {
                    pos2 = i;
                    break;
                }
            }
            swap(a[pos1],a[pos2]);
            for(int i = 0; i < k; i++)
                ans2 = ans * a[i] % MOD;
            ans = max(ans1,ans2);
        }
    }
    ans = ans % MOD;
//    cout << ans << endl;
    if(ans < 0)
    {
        if(flag)
            ans = 0;
        else
            ans += MOD;
    }
    cout << ans << endl;
    return 0;
}