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)

N, K = [int(i) for i in input().split()]
A = [int(i) for i in input().split()]
M = 10**9 + 7
if N == K:
    result = 1
    for i in range(K):
        result = result * A[i] % M
    print(result)
    exit()
minus = [i for i in A if i < 0]
l_minus = len(minus)
plus = [i for i in A if i >= 0]
l_plus = len(plus)
plus.sort(reverse=1)
minus.sort()
if len(plus) == 0 and K % 2 == 1:
    result = 1
    for i in range(K):
        result = result * minus[-i-1] % M
    print(result)
    exit()

m_x = 0
p_x = 0
max_mm = -1
if (m_x+1) * 2 <= l_minus:
    max_mm = minus[m_x * 2] * minus[m_x * 2 + 1]
max_pp = -1
if (p_x+1) * 2 <= l_plus:
    max_pp = plus[p_x * 2] * plus[p_x * 2 + 1]
counter = 0
array = []
while counter * 2 + 1 <= K:
    if max_pp > max_mm:
        array.append(plus[p_x * 2])
        array.append(plus[p_x * 2 + 1])
        p_x += 1
        if (p_x+1) * 2 <= l_plus:
            max_pp = plus[p_x * 2] * plus[p_x * 2 + 1]
        else:
            max_pp = -1

    else:
        array.append(minus[m_x * 2])
        array.append(minus[m_x * 2 + 1])
        m_x += 1
        if (m_x+1) * 2 <= l_minus:
            max_mm = minus[m_x * 2] * minus[m_x * 2 + 1]
        else:
            max_mm = -1
    counter += 1
if K%2 == 1:
    array.append(plus[p_x * 2])
result = 1
for each in array:
    result = result * each % M
print(result)