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: Accepted)

from functools import reduce

n, k = map(int, input().split())
a = list(map(int, input().split()))

mod = 10 ** 9 + 7
if n == k:
    print(reduce(lambda ac, v: ac * v % mod, a, 1))
    exit()

a.sort(key=lambda v: abs(v), reverse=True)
if len(list(filter(lambda v: v < 0, a))) == n and k % 2 == 1:
    print(reduce(lambda ac, v: ac * v % mod, a[n - k :], 1))
    exit()

ans = 1
mn = 0
for v in a[:k]:
    if v < 0:
        mn += 1
    ans *= abs(v)
    ans %= mod

if mn % 2 == 0:
    print(ans)
    exit()

mnp, mnn = 0, 0
for v in a[k - 1 :: -1]:
    if mnp != 0 and mnn != 0:
        break
    elif mnp == 0 and v > 0:
        mnp = v
    elif mnn == 0 and v < 0:
        mnn = v
mxp, mxn = 0, 0
for v in a[k:]:
    if mxp != 0 and mxn != 0:
        break
    elif mxp == 0 and v > 0:
        mxp = v
    elif mxn == 0 and v < 0:
        mxn = v
x, y = mxp, mnn
if mnp != 0 and mxn * mnn > mxp * mnp:
    x, y = mxn, mnp
ans *= pow(abs(y), mod - 2, mod)
ans %= mod
ans *= abs(x)
ans %= mod
print(ans)