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 Python (3.8.2) (judge verdict: Wrong Answer)

import numpy as np
N,K = map(int,input().split())
import math
A = list(map(int,input().split()))
flag = 0
if 0 in A:
    flag = 1
A.sort()

plus = list(filter(lambda x:x>0, A))[::-1]
plus = np.log10(plus,dtype="float128")

from itertools import accumulate
acc_plu = [0] +  list(accumulate(plus))
minu = filter(lambda x:x<0, A)
minu = list(map(lambda x:-x,minu))
minu = np.log10(minu,dtype="float128")
acc_min = [0] +  list(accumulate(minu))


if K % 2 == 0 : num = K // 2 + 1
else: num = (K + 1) // 2 
cand = []
x = K
y = 0
MOD = 10**9 +7
for i in range(num):
    try:
        cand.append((acc_plu[x] +  acc_min[y],x ,y ))
    except: pass
    x -= 2 
    y += 2

ans = 1
if cand == []:
    if flag:
        print(0)
        exit()
    cnt = 0
    #マイナス確定
    abss = sorted(list(map(lambda x :abs(x),A)))
    for x in abss:
        if cnt == K:break
        ans *= x
        ans %= MOD
        cnt += 1
    ans *= -1
    ans %= MOD
    print(ans)
else:
    cand = sorted(cand)[::-1]
    plus = list(filter(lambda x:x>0, A))[::-1]
    minu = list(filter(lambda x:x<0, A))
    c = cand[0]
    ans = 1
    for i in range(c[1]):
        ans *= plus[i]
        ans %= MOD
    for i in range(c[2]):
        ans *= minu[i]
        ans %= MOD
    print(ans)