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)

#!/usr/bin/env python
# -*- coding: utf-8 -*-

import sys
sys.setrecursionlimit(10**7)
from pprint import pprint as pp
from pprint import pformat as pf
# @pysnooper.snoop()
#import pysnooper # debug

import math
#from sortedcontainers import SortedList, SortedDict, SortedSet # no in atcoder
import bisect

class ModInt(int):

    MOD = 10 ** 9 + 7

    def __add__(self, other):
        self = ModInt(int.__add__(self, other) % ModInt.MOD)
        return self

    def __mul__(self, other):
        self = ModInt(int.__mul__(self, other) % ModInt.MOD)
        return self

def mysplit(data):
    ps = [] # include 0
    ms = []
    for d in data:
        if d < 0:
            ms.append(ModInt(d))
        else:
            ps.append(ModInt(d))
    return list(reversed(sorted(ps))), sorted(ms)

def small_abs(ms, k):
    ans = ModInt(1)
    ms = list(reversed(ms))
    for i in range(k):
        ans *= ms[i]
    return ans

def take_p(ans, k, ps, pk):
    ans *= ps[pk]
    pk += 1
    return ans, k - 1, pk

def take_m(ans, k, ms, mk, sign_p):
    ans *= ms[mk]
    mk += 1
    return ans, k - 1, mk, sign_p

def take_all_m(ans, k, ms, mk, sign_p):
    while k > 0:
        ans, k, mk, sign_p = take_m(ans, k, ms, mk, sign_p)
    return ans

def solve(data, k):
    ps, ms = mysplit(data)
    if len(ps) == 0:
        return small_abs(ms, k)
    ans = ModInt(1)
    sign_p = True
    pk = 0
    mk = 0
    while k > 0:
        if pk == len(ps) - 1: # last p
            if k % 2 == 1:
                ans, k, pk = take_p(ans, k, ps, pk)
                k -= 1
                #print('hoge') # debug
            return take_all_m(ans, k, ms, mk, sign_p)
        if mk >= len(ms) or ps[pk] > -1 * ms[mk]:
            ans, k, pk = take_p(ans, k, ps, pk)
        else:
            ans, k, mk, sign_p = take_m(ans, k, ms, mk, sign_p)
    return ans



if __name__ == '__main__':
    n, k = list(map(int, input().split()))
    data = list(map(int, input().split()))
    ans = solve(data, k)
    #print('ans') # debug
    print(ans)



    #print('\33[32m' + 'end' + '\033[0m') # debug