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)

n, k = map(int, input().split())
modulo = 10 ** 9 + 7
*arr, = map(int, input().split())
inverses = [pow(v, modulo - 2, modulo) for v in arr]
neg_cnt = 0
for v in arr:
    if v < 0:
        neg_cnt += 1

def min_pos(arr):
    pass


if k == n:
    res = 1
    for v in arr:
        res *= v
        res %= modulo
    print(res)
elif neg_cnt == n and k % 2 == 1:
    res = 1
    arr.sort(reverse=True)
    for i in range(k):
        res *= arr[i]
        res %= modulo
    print(res)
else:
    pos = []
    neg = []
    for i, v in enumerate(arr):
        if v < 0:
            neg.append(i)
        else:
            pos.append(i)

    neg.sort(key=lambda v: abs(arr[v]), reverse=True)
    pos.sort(key=lambda v: abs(arr[v]), reverse=True)

    res = 1
    i = 0
    j = 0
    while i + j < k and (i < len(pos) - 1 or j < len(neg) - 1):
        if j >= len(neg) - 1 or i < len(pos) - 1 and arr[pos[i]] * arr[pos[i + 1]] > arr[neg[j]] * arr[neg[j + 1]]:
            res *= arr[pos[i]]
            res *= arr[pos[i + 1]]
            i += 2
        else:
            res *= arr[neg[j]]
            res *= arr[neg[j + 1]]
            j += 2
        res %= modulo

    while i + j < k:
        res *= arr[pos[i]]
        i += 1
        res %= modulo

    print(res)