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: Runtime Error)

//#include "testlib.h"
//#include <spoj.h>

#include <iostream>
#include <stdio.h>
#include <vector>
#include <string>
#include <algorithm>
#include <math.h>
#include <assert.h>
#include <time.h>
#include <memory.h>
#include <set>
#include <numeric>
#include <map>
#include <queue>
#include <stack>
#include <bitset>
#include <unordered_map>

using namespace std;

const int mod = 1e9+7;

int a[111111];

int cmp(int a, int b) {
    return abs(b) > abs(a);
}

int main() {
    ios::sync_with_stdio(0);
    int t = 1, sn = 0;
    //cin >> t; assert(1 <= t && t <= 1e5);
    while (t --> 0) {
        int n, k;
        cin >> n >> k;
        assert(1 <= k && k <= n && n <= 1e5); sn += n;
        assert(sn <= 5e5);
        bool zero = 0;
        for(int i = 0; i < n; ++i) {
            cin >> a[i];
            assert(-1e9 <= a[i] && a[i] <= 1e9);
            zero |= (a[i] == 0);
        }
        sort(a, a+n, cmp);
        
//        for(int i = 0; i < n; ++i) {
//            cout << a[i] << " ";
//            if (i == n-k-1)
//                cout << "\n";
//        }
//        cout << "\n";
        
        int sn = 1;
        vector<int> nums;
        int gneg = -1e9-1, gpos = 1e9+1;
        for(int i = 0, id = n-1; i < k; ++i, id--) {
            if (a[id] < 0) sn *= -1;
            nums.push_back(a[id]);
            if (a[id] < 0)
                gneg = max(gneg, a[id]);
            else
                gpos = min(gpos, a[id]);
        }
        
        if (sn > 0) {
            int ans = 1;
            for(auto x : nums)
                ans = (ans * 1ll * x) % mod;
            cout << (ans + mod) % mod << "\n";
        } else {
            int mn = 1, mx = -1;
            for(int i = 0; i < n-k; ++i) {
                mn = min(mn, a[i]);
                mx = max(mx, a[i]);
            }
            
            //cout << gneg << " " << mx << "\n";
            //cout << gpos << " " << mn << "\n";
            
            bool g1 = gneg != -1e-9-1 && mx != -1;
            bool g2 = gpos != 1e9+1 && mn != 1;
            if (g1 && g2) {
                int val, repl;
                if (mx * 1ll * gpos > mn * 1ll * gneg)
                    val = gneg, repl = mx;
                else
                    val = gpos, repl = mn;
                
                for(int i = 0; i < k; ++i)
                    if (nums[i] == val) {
                        nums[i] = repl;
                        break;
                    }
                int ans = 1;
                for(auto x : nums)
                    ans = (ans * 1ll * x) % mod;
                cout << (ans + mod) % mod << "\n";
            } else if (g1) {
                for(int i = 0; i < k; ++i)
                    if (nums[i] == gneg) {
                        nums[i] = mx;
                        break;
                    }
                int ans = 1;
                for(auto x : nums)
                    ans = (ans * 1ll * x) % mod;
                cout << (ans + mod) % mod << "\n";
            } else if (g2) {
                for(int i = 0; i < k; ++i)
                    if (nums[i] == gpos) {
                        nums[i] = mn;
                        break;
                    }
                int ans = 1;
                for(auto x : nums)
                    ans = (ans * 1ll * x) % mod;
                cout << (ans + mod) % mod << "\n";
            } else {
                if (zero)
                    cout << "0\n";
                else {
                    int ans = 1;
                    for(int i = 0; i < k; ++i)
                        ans = (ans * 1ll * a[i]) % mod;
                    cout << (ans + mod) % mod << "\n";
                }
            }
            
            
        }
    }
    return 0;
}