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)

#! /usr/bin/env python3

import sys
import numpy as np
int1 = lambda x: int(x) - 1
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(500000)
MOD = pow(10, 9) + 7

N, K, *A = map(int, read().split())

if K == N:
    ans = 1
    for a in A:
        ans *= a
        ans %= MOD
    print(ans)
    sys.exit()

A_pos = [a for a in A if a >= 0]
A_neg = [a for a in A if a < 0]

if len(A_pos) == 0:
    if K % 2 == 1:
        A = sorted(A, key=lambda x: abs(x))
    else:
        A = sorted(A, key=lambda x: -abs(x))
    ans = 1
    for a in A_neg[:K]:
        ans *= a
        ans %= MOD
    print(ans)
    sys.exit()

A_pos = sorted(A_pos, key=lambda x: -abs(x))
A_neg = sorted(A_neg, key=lambda x: -abs(x))
ans = 1
r = K
if r % 2 == 1:
    ans *= A_pos[0]
    ans %= MOD
    A_pos = A_pos[1:]
    r -= 1

while r > 0:
    if len(A_pos) <= 1:
        ans *= A_neg[0] * A_neg[1]
        ans %= MOD
    elif len(A_neg) <= 1:
        ans *= A_pos[0] * A_pos[1]
        ans %= MOD
    else:
        acc_pos = A_pos[0] * A_pos[1]
        acc_neg = A_neg[0] * A_neg[1]

    if acc_pos > acc_neg:
        ans *= acc_pos
        ans %= MOD
    else:
        ans *= acc_neg
        ans %= MOD
    r -= 2
print(ans % MOD)