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

if max(a) < 0:
    a.sort()
    ans = 1
    if k % 2 == 0:
        for e in a[:k]:
            ans *= e
            ans %= mod
    else:
        for e in a[-k:]:
            ans *= e
            ans %= mod

    print(ans)

else:
    neg = []
    pos = []
    for e in a:
        if e < 0:
            neg.append(e)
        else:
            pos.append(e)

    neg.sort()
    pos.sort(reverse=True)

    ans = 1
    if k % 2:
        ans *= pos.pop(0)
        k -= 1

    nums = [e1 * e2 for e1, e2 in zip(neg[::2], neg[1::2])]
    nums += [e1 * e2 for e1, e2 in zip(pos[::2], pos[1::2])]

    nums.sort(reverse=True)
    for e in nums[:k//2]:
        ans *= e
        ans %= mod

    print(ans)