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: Runtime Error)

from functools import reduce
import operator
MOD = 10**9+7
product = lambda it: reduce(lambda x,y: (x*y)%MOD,it,1)

N,K = map(int,input().split())
A = list(map(int,input().split()))

from fractions import Fraction

def solve():
    if N == K:
        return product(A)

    if all(v < 0 for v in A):
        A.sort()
        return product(A[-K:])

    A.sort(key=lambda x: abs(x))

    if A[-K] == 0:
        return 0

    parity = sum(v < 0 for v in A[-K:])%2
    if parity == 0:
        return product(A[-K:])

    fp = N-K
    while fp < N and A[fp] < 0:
        fp += 1

    fn = N-K
    while fn < N and A[fn] > 0:
        fn += 1


    lp = N-K-1
    while lp >= 0 and A[lp] < 0:
        lp -= 1

    ln = N-K-1
    while ln >= 0 and A[ln] > 0:
        ln -= 1

    if fp < N and ln >= 0:
        r1 = Fraction(-A[ln],A[fp])
    else:
        r1 = 0
    if fn < N and lp >= 0:
        r2 = Fraction(-A[lp],A[fn])
    else:
        r2 = 0
    if r1 > r2:
        return (product(A[-K:])*A[ln]*pow(A[fp],-1,MOD))%MOD
    else:
        return (product(A[-K:])*A[lp]*pow(A[fn],-1,MOD))%MOD

print(solve())