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)

from heapq import heappop, heappush
mod = 10**9+7
n, k = map(int, input().split())
a = [int(x) for x in input().split()]

pl = []
mn = []
zr = []

tmp = 1
cnt = 0

for x in a:
    if x > 0:
        pl.append(x)
    elif x < 0:
        mn.append(-x)
    else:
        zr.append(x)

pl = sorted(pl, reverse=True)
mn = sorted(mn, reverse=True)

ans = 0

if len(mn) >= k and k % 2:
    tmp = 1
    for i in range(1, k+1):
        tmp *= mn[-i]
        tmp %= mod
    ans = -tmp

if len(zr) > 0:
    ans = max(0, ans)

pl_cum = [1]
for i, x in enumerate(pl):
    pl_cum.append(pl_cum[-1]*x % mod)

mn_cum = [1]
for i, x in enumerate(mn):
    mn_cum.append(mn_cum[-1]*x % mod)

for p in range(0, k+1, 2):
    if len(mn) < p:
        break
    if len(pl) >= k-p:
        ans = max(pl_cum[k-p]*mn_cum[p] % mod, ans)

print(ans % mod)