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()))
ans =1

if n == k:
   for i in a:
       ans *= i
       if abs(ans) >10**9+7:
           ans = ans%(10**9+7)

elif all(i <= 0 for i in a) and k%2 ==1:
    a.sort(reverse = True)
    for i in range(k):
        ans *= a[i]
        if abs(ans) > 10 ** 9 + 7:
            ans = ans % (10 ** 9 + 7)

else:
    am =[-10**8]
    ap =[10**8]

    a.sort(key = abs,reverse = True)
    amax = a[:k]
    amin = a[k:]
    c=1
    if 0 in amax:
        ans = 0
    else:
        for i in amax:
            if i<0:
                am.append(i)
                c *=-1
            elif i>0:
                ap.append(i)
        if c ==1:
            for i in amax:
                ans *= i
                if abs(ans) > 10 ** 9 + 7:
                    ans = ans % (10 ** 9 + 7)
        else:

            if min(amin)/min(ap) > max(amin)/max(am):
                amax.remove(max(am))
                amax.append(max(amin))
            else:
                amax.remove(min(ap))
                amax.append(min(amin))
            for i in amax:
                ans *= i
                if abs(ans) > 10 ** 9 + 7:
                    ans = ans % (10 ** 9 + 7)

print(ans% (10 ** 9 + 7))