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)

def make_set_list(array,valid):
    new_array = []
    for i in range(len(array)//2):
        new_array.append(array[2*i]*array[2*i+1])
    if len(array)%2 == 1 and valid == 1:
        new_array.append(array[len(array)-1])
    return new_array

N, K = list(map(int,input().split()))
As = list(map(int,input().split()))
p_nums = []
n_nums = []
for i in range(N):
    n = As[i]
    if n < 0:
        n_nums.append(n)
    else:
        p_nums.append(n)
As.sort(key = abs)
n_nums.sort()
p_nums.sort(reverse = True)
if len(p_nums) > 0:
    if N > K:
        ok = True
    elif len(n_nums) % 2 == 0:
        ok = True
    else:
        ok = False
elif K % 2 == 0:
    ok = True
else:
    ok = False

ans = 1

if ok:
    if K % 2 == 0:
        set_p_num = make_set_list(p_nums,1)
        set_n_num = make_set_list(n_nums,0)
        set_num = set_p_num + set_n_num
        set_num.sort(reverse = True)
        for i in range(K//2):
            ans = (ans*(set_num[i]%(10**9+7)))%(10**9+7)
    else:
        ans = p_nums.pop(0)
        set_p_num = make_set_list(p_nums,1)
        set_n_num = make_set_list(n_nums,0)
        set_num = set_p_num + set_n_num
        set_num.sort(reverse = True)
        for i in range(K//2):
            ans = (ans*(set_num[i]%(10**9+7)))%(10**9+7)
else:
    for i in range(K):
        ans = (ans*(As[i]%(10**9+7)))%(10**9+7)

print(ans)