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)

a, b = map(int,input().split())
li = list(map(int,input().split()))

xx = 10**9+7
li = sorted(li,key = abs)

def mut(lis):
    res = 1
    for i in lis:
        res*=i
    return res

if all([i<0 for i in li]):
    res = 1
    for i in li[:b]:
        res *= i
    print (int(res%xx))
else:
    res1,res2 = 0,0
    if mut(li[-b:])<0:
        for i in range(b):
            if li[-i]<0:
                res1 = 1/li[-i]
            elif li[-i]>0:
                res2 = 1/li[-i]
        for i in range(len(li) - b):
            if li[i]<0:
                res1 *= li[i]
            elif li[i]>0:
                res2 *= li[i]
        print(int(mut(li[-b:])*max(res1,res2)%xx))
    else:
        print(int(mut(li[-b:])%xx))