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 ll MAXN=2e5+10,MOD=1e9+7;
ll K,N,Neg[MAXN],Pos[MAXN],CntNeg,CntPos;
inline ll fpow(ll a,ll x){
    ll ans=1;
    for(;x;x>>=1,a=a*a%MOD) if(x&1) ans=ans*a%MOD;
    return ans;
}
inline ll ans(){
    if(CntNeg+CntPos<K) return 0;

    if(CntPos==0){
        if((K&1)&&(N-CntNeg)) return 0;
        if(K&1)
            sort(Neg+1,Neg+1+CntNeg,[](int a,int b){ return a>b; });
        else
            sort(Neg+1,Neg+1+CntNeg,[](int a,int b){ return a<b; });
        ll Ans=1;
        for(int i=1;i<=K;i++) Ans=Ans*Neg[i]%MOD;
        return Ans;
    }

    if(CntNeg<=1){
        sort(Pos+1,Pos+1+CntPos,[](int a,int b){ return a>b; });
        ll Ans=1;
        for(int i=1;i<=K;i++) Ans=Ans*Pos[i]%MOD;
        return Ans;
    }

    sort(Pos+1,Pos+1+CntPos,[](int a,int b){ return a>b; });
    sort(Neg+1,Neg+1+CntNeg,[](int a,int b){ return a<b; });
    CntNeg-=CntNeg&1;
    ll Ans=1,CurPos=1,CurNeg=1,Cnt=K,LstPos;
    Pos[CntPos+1]=1;
    while(CurPos<=CntPos&&Cnt>3){
        if(CurNeg<=CntNeg-1&&Pos[CurPos]*Pos[CurPos+1]<=Neg[CurNeg]*Neg[CurNeg+1]){
            Ans=Neg[CurNeg]*Neg[CurNeg+1]%MOD*Ans%MOD;
            CurNeg+=2;
            Cnt-=2;
            continue;
        }
        LstPos=Pos[CurPos];
        Ans=Ans*Pos[CurPos++]%MOD;
        Cnt--;
    }
    if(Cnt==3){
        if(CurNeg>CntNeg)
            return Pos[CurPos]*Pos[CurPos+1]%MOD*Pos[CurPos+2]%MOD*Ans%MOD;
        Ans=Ans*Pos[CurPos++]%MOD;
    }
    if(Cnt==2){
        if(CurNeg<=CntNeg-1){
            if(CurPos>=CntPos)
                return Neg[CurNeg]*Neg[CurNeg+1]%MOD*Ans%MOD;
            else if(Pos[CurPos]*Pos[CurPos+1]<=Neg[CurNeg]*Neg[CurNeg+1])
                return Neg[CurNeg]*Neg[CurNeg+1]%MOD*Ans%MOD;
            else
                return Pos[CurPos]*Pos[CurPos+1]%MOD*Ans%MOD;
        }
        return Pos[CurPos]*Pos[CurPos+1]%MOD*Ans%MOD;
    }

    if(Cnt&1) Cnt++,Ans*=fpow(LstPos,MOD-2);
    while(Cnt)
        Ans=Ans*Neg[CurNeg++]%MOD,Cnt--;
    return Ans;
}
int main(){
    cin>>N>>K;
    for(int i=1;i<=N;i++){
        int A;
        cin>>A;
        if(A>0) Pos[++CntPos]=A;
        else if(A<0) Neg[++CntNeg]=A;
    }
    cout<<(MOD+ans()%MOD)%MOD<<endl;
    return 0;
}