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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

from math import ceil
from collections import defaultdict as dd
import sys
input=sys.stdin.readline
#t=int(input())
#while t:
n,k=map(int,input().split())
positive=[]
negative=[]
zero=[]
mod=10**9+7
l=list(map(int,input().split()))
l.sort(reverse=True)
for i in range(n):
    if(l[i]>0):
        positive.append(l[i])
    elif(l[i]==0):
        zero.append(0)
    else:
        negative.append(l[i])
positive.sort()
negative.sort(reverse=True)
com=[]
for i in range(len(negative)-1,-1,-2):
    com.append(abs(negative[i]))
    com.append(abs(negative[i-1]))
#print(com)
lp=len(positive)
ln=len(negative)
lc=len(com)
lz=len(zero)
mul=1
if(k%2==0):
    i=lp-1
    j=lc-1
    while(k and j>0 and i>0):
        if(com[j]*com[j-1]>positive[i]*positive[i-1]):
            mul=(mul*com[j]*com[j-1])%mod
            j-=2
        else:
            mul=(mul*positive[i]*positive[i-1])%mod
            i-=2
        k-=2
    while (k and i>0):
        mul=(mul*positive[i]*positive[i-1])%mod
        i-=2
        k-=2
    while(k and j>0):
        mul=(mul*com[j]*com[j-1])%mod
        j-=2
        k-=2
    if(k):
        mul=0
else:
    i=lp-1
    j=lc-1
    if(positive):
        mul=positive.pop()
        i-=1
        k-=1
        while(k and j>0 and i>0):
            if(com[j]*com[j-1]>positive[i]*positive[i-1]):
                mul=(mul*com[j]*com[j-1])%mod
                j-=2
            else:
                mul=(mul*positive[i]*positive[i-1])%mod
                i-=2
            k-=2
        while (k and i>0):
            mul=(mul*positive[i]*positive[i-1])%mod
            i-=2
            k-=2
        while(k and j>0):
            mul=(mul*com[j]*com[j-1])%mod
            j-=2
            k-=2
        if(k):
            mul=0
    else:
        mul=1
        kk=k
        if(lz):
            mul=0
        else:
            for i in range(min(k,ln)):
                #print(negative[i])
                mul=((mul%mod)*((negative[i]+mod)%mod))%mod
                kk-=1
            if(kk):
                mul=0
print(mul)