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: Wrong Answer)

import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

n, k = map(int, input().split())
a = list(map(int, input().split()))
MOD = 10 ** 9 + 7

plus_zero = []
minus = []

for i in a:
    if i >= 0:
        plus_zero.append(i)
    if i < 0:
        minus.append(-i)

from collections import deque

plus_zero = deque(sorted(plus_zero, reverse=True))
minus = deque(sorted(minus, reverse=True))
absolute = deque(sorted(a, key=abs, reverse=True))

ans_lst = []
# 境界条件: k == n
if k == n:
    ans_lst.extend(a)
# 負
elif len(plus_zero) == 0 and (k % 2) != 0:
    for _ in range(k):
        ans_lst.append(-minus.pop())
# 正 or 0
else:
    minus_num = 0
    for _ in range(k):
        v = absolute.popleft()
        if v < 0:
            minus_num += 1
        ans_lst.append(v)
    if minus_num % 2 != 0:
        abs_min_plus_zero, abs_min_minus = None, None
        abs_max_plus_zero, abs_max_minus = None, None
        for i in ans_lst:
            if i >= 0:
                if abs_min_plus_zero is None:
                    abs_min_plus_zero = i
                else:
                    abs_min_plus_zero = min(i, abs_min_plus_zero)
            else:
                if abs_min_minus is None:
                    abs_min_minus = i
                else:
                    abs_min_minus = max(abs_min_minus, i)
        for i in absolute:
            if i >= 0:
                if abs_max_plus_zero is None:
                    abs_max_plus_zero = i
                else:
                    abs_max_plus_zero = max(i, abs_max_plus_zero)
            else:
                if abs_max_minus is None:
                    abs_max_minus = i
                else:
                    abs_max_minus = min(abs_max_minus, i)
        case1, case2 = False, False
        if abs_min_plus_zero is not None and abs_max_minus is not None:
            case1 = True
        if abs_min_minus is not None and abs_max_plus_zero is not None:
            case2 = True
        if case1 and case2:
            pass
        #    if abs_max_minus * abs_min_minus <= abs_max_plus_zero * abs_min_plus_zero:
        #        ans_lst.remove(abs_min_minus)
        #        ans_lst.append(abs_max_plus_zero)
        #    else:
        #        ans_lst.remove(abs_min_plus_zero)
        #        ans_lst.append(abs_max_minus)
        elif case1:
            ans_lst.remove(abs_min_plus_zero)
            ans_lst.append(abs_max_minus)
        #elif case2:
        #    ans_lst.remove(abs_min_minus)
        #    ans_lst.append(abs_max_plus_zero)


# functools.reduceはTLEをくらう場合があるので気をつける
ans = 1
for i in ans_lst:
    ans = (ans * i) % MOD
print(ans)