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 math

def Next(): return input()
def NextInt(): return int(Next())
def NextInts(): return map(int,input().split())
def Nexts(): return map(str,input().split())
def NextIntList(): return list(map(int,input().split()))
def RowInts(n): return [input() for i in range(n)]

def solve():
    n, k = NextInts()
    da = NextIntList()
    ans = 1
    MOD = 10**9+7
    
    if n == k:
        for i in range(n):
            ans = ans*da[i]%MOD
        return ans
    
    neg = []
    pos = []
    for i in range(n):
        if da[i] < 0:
            neg.append(da[i])
        else:
            pos.append(da[i])
    neg.sort()
    pos.sort()

    if len(pos) == 0 and k%2 == 1:
        neg.reverse()
        for i in range(k):
            ans = ans * neg[i] % MOD
        return ans
    
    pos.reverse()
    li = []
    po, ne = 0, 0
    if k%2 == 1:
        po = 1
        ans = pos[0]
    while po+1 < len(pos):
        li.append(pos[po]*pos[po+1])
        po += 2
    while ne+1 < len(neg):
        li.append(neg[ne]*neg[ne+1])
        ne += 2
    li.sort()
    li.reverse()
    for i in range(k//2):
        ans = li[i] * ans % MOD
    return ans

if __name__ == "__main__":
    print(solve())