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 sys
import numpy as np

readline = sys.stdin.buffer.readline

N, K = map(int, readline().split())
A = np.array(list(map(int, readline().split())), dtype=np.int64)
MOD = 10 ** 9 + 7

B = np.zeros(N, dtype=np.int64)
B[A > 0] = 1
B[A < 0] = -1

# 全部負かつKが奇数のときは場合分け
if len(B[A > 0]) == 0 and K % 2 == 1:
    f = 1
else:
    f = 0

C = np.zeros([2, N], dtype=np.int64)
C[0] = np.abs(A)
C[1] = B

C = C[:, np.argsort(C[0])[::-1]]

ans = 1

# 選んだ中から一番小さい正の数と負の数を記憶
minus_m = 10 ** 9
plus_m = 10 ** 9

if f == 0:
    for i in range(K):
        ans *= C[0, i] * C[1, i]
        ans %= MOD

        if C[1, i] == 1:
            if plus_m > C[0, i]:
                plus_m = C[0, i]

        elif C[1, i] == -1:
            if minus_m > C[0, i]:
                minus_m = C[0, i]

    if ans < 0:
        mm = 0
        MM = 0
        q = C[:, K:]
        p = [q[1] == 1]
        pp = q[p]
        MM = np.max(pp)

        q = C[:, K:]
        p = [q[1] == -1]
        pp = q[p]
        mm = np.max(pp)

        if plus_m * MM > minus_m * mm:
            ans = ans // plus_m
            ans *= MM
        else:
            ans = ans // minus_m
            ans *= mm

else:
    C = C[0][::-1]
    for i in range(K):
        ans *= C[i]

    ans = -ans


print(ans % MOD)