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;
typedef long long LL;
const int maxn=2e5+100;
const int mod=1e9+7;
const int INF=0x3f3f3f3f;
int A[maxn];
int T,n,m,k;
 
int main()
{
    cin>>n>>k;
    int cnt1=0,cnt2=0,cnt3=0;
    LL res=1;
    for(int i=1;i<=n;i++)
    {
        cin>>A[i];
        if(A[i]<0) cnt1++;
        if(A[i]==0) cnt2++;
        if(A[i]>0) cnt3++;
    }
    sort(A+1,A+1+n);
    LL res1=1;
    for(int i=n;i>n-k;i--)
        res1=res1*A[i]%mod;
    int l=1,r=n;
    while(k)
    {
        if(k>=2&&1LL*A[l]*A[l+1]>=1LL*A[r]*A[r-1])
        {
            res=res*A[l]*A[l+1]%mod;
            l+=2;
            k-=2;
        }
        else
        {
            res=res*A[r]%mod;
            r-=1;
            k-=1;
        }
    }
    if(res<0&&cnt2) res=0;
    if(res<res1&&!cnt2) res=res1;
    cout<<(res+mod)%mod<<endl;
}