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: Accepted)

from collections import deque
import sys
input=sys.stdin.readline

mod=10**9+7
n,k=map(int,input().split())
A=list(map(int,input().split()))
cnt=k

B,C=[],[]
for i in range(n):
    num=A[i]
    if num>=0:B.append(num)
    else:C.append(num)

B.sort(reverse=True)
C.sort()
B,C=deque(B),deque(C)

ans,flag=1,1
while k!=0:
    num=0
    length_B,length_C=len(B),len(C)
    if k>=2:
        if length_B>=2 and length_C>=2:
            plus=B[0]*B[1]
            negative=C[0]*C[1]
            if plus>negative:
                ans *=B.popleft()
                num=1
            else:ans *=C.popleft()*C.popleft()
        elif length_C>=2:ans *=C.popleft()*C.popleft()
        elif length_B>=2:ans *=B.popleft()*B.popleft()
        else:
            ans *=B.popleft()*C.popleft()
            flag=0
        k -=2-num
    else:
        if 0<length_B:ans *=B.popleft()
        elif 0<length_C:
            ans *=C.popleft()
            flag=0
        k -=1
    ans %=mod

if flag:print(ans);exit()

ans=1
A=sorted(A,key=lambda x:abs(x))
for i in range(cnt):
    ans *=A[i]
    ans %=mod
print(ans)