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 Python (3.8.2) (judge verdict: Runtime Error)

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

a_p =[]
a_m =[]
for i in a:
    if i >= 0:
        a_p.append(i)
    else :
        a_m.append(i)

a_p.sort()
a_m.sort(reverse=True)


a_select =[]

if len(a_p) == 0:
    for i in range(k):
        a_select.append(a_m[i])


while len(a_select) < k:
    if len(a_select) == k - 1:
        a_select.append(a_p[-1])
        break
    if len(a_p) == 1 and (k-len(a_select))%2 == 1:
        a_select.append(a_p[-1])
    elif len(a_p) == 0:
        a_select.append(a_m.pop(-1))
    elif len(a_m) <= 1:
        a_select.append(a_p.pop(-1))
    elif a_p[-1]*a_p[-2] > a_m[-1]*a_m[-2] :
        a_select.append(a_p.pop(-1))
    else:
        a_select.append(a_m.pop(-1))
        a_select.append(a_m.pop(-1))

print(a_select)
ans = 1
for i in a_select:
    ans = ans*i % (10**9 + 7)

print(ans)