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: Runtime Error)

# coding: utf-8
import sys
# from operator import itemgetter
sysread = sys.stdin.readline
read = sys.stdin.read
sys.setrecursionlimit(10 ** 7)
from heapq import heappop, heappush
#from collections import OrderedDict, defaultdict
#import math
#from itertools import product, accumulate, combinations, product
#import bisect# lower_bound etc
#import numpy as np
#from copy import deepcopy
#from collections import deque
#import numba

def run():
    N, K = list(map(int, input().split()))
    A = list(map(int, sysread().split()))
    mod = 10 ** 9 + 7

    plus = [a for a in A if a >= 0]
    minus = [-a for a in A if a < 0]

    plus = sorted(plus, reverse=True)
    minus = sorted(minus, reverse=True)

    P, M  = [1], [1]
    for p in plus:
        P.append((P[-1] * p) % mod)
    for m in minus:
        M.append(((M[-1] * (-m)) % mod))
    #print(P, M)
    max_ans = -1

    for i in range(K, -1, -2):
        if len(plus) < i:continue
        if len(minus) < K - i:continue
        if max_ans == -1:
            max_ans = P[i] * M[K-i] % mod
        else:
            if not plus[i] or not plus[i + 1]:
                max_ans = P[i] * M[K-i] % mod
            if plus[i+1] / minus[K-i-1] < minus[K-i-2] / plus[i]:
                max_ans = P[i] * M[K-i] % mod

    if max_ans == -1:
        plus = plus[::-1]
        minus = minus[::-1]
        P, M = [1], [1]
        for p in plus:
            P.append((P[-1] * p) % mod)
        for m in minus:
            M.append(((M[-1] * (-m)) % mod))

        for i in range(K-1, -1, -2):
            if len(plus) < i: continue
            if len(minus) < K - i: continue
            if max_ans == -1:
                max_ans = P[i] * M[K - i] % mod
            else:
                if not plus[i] or not plus[i+1]:
                    max_ans = 0
                    break
                if plus[i + 1] / minus[K - i - 1] > minus[K - i - 2] / plus[i]:
                    max_ans = P[i] * M[K - i] % mod

    print(max_ans)

if __name__ == "__main__":
    run()