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: Wrong Answer)

import functools

def sign(x):
    if x>0:
        return 1
    elif x==0:
        return 0
    else:
        return -1
    
def multiply(x,y):
    ans = x*y
    if ans>=10**9+7:
        ans %= (10**9+7)
    return ans

N,K = map(int,input().split())
A = list(map(int,input().split()))
A.sort()

if (A[-1]<0 and K%2==1) or K==N:
    combi = A[-K:]
    if K >1:
        answer =  functools.reduce(multiply,map(abs,combi[1:]))
        answer *= combi[0]
    else:
        answer = combi[0]
    answer %= 10**9+7
else:
    signs = 1
    i,j = 0,0
    for _ in range(K):
        if abs(A[i]) > abs(A[N-j-1]):
            signs *= sign(A[i])
            i += 1
            
        else:
            signs *= sign(A[N-j-1])
            j += 1
    combi = A[N-j:] + A[:i]
    del A[N-j:]
    del A[:i]
    combi = combi[::-1]     
       
    if signs == -1:
        if A:
            if A[0]>=0:
                del combi[0]
                combi.append(A[-1])
            elif A[0]<0 and A[-1] >0:
                if combi[0]*A[0] > combi[-1]*A[-1]:
                    del combi[-1]
                    combi.insert(0,A[0])
                else:
                    del combi[0]
                    combi.append(A[-1])
            elif A[-1] <= 0:
                del combi[-1]
                combi.insert(0,A[0]) 
                
    answer =  functools.reduce(multiply,map(abs,combi))
print(answer)