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)

nums=input().rstrip().split()
num=int(nums[0])
k=int(nums[1])
mains=input().rstrip().split()
mai=[]
for i in range(len(mains)):
    mai.append(int(mains[i]))
main=sorted(mai,key=abs,reverse=True)
result=1
def findplus_plus(x):
    for i in range(x,len(main)-1):
        if main[i]>=0:
            return main[i]
    return -1
def findplus_minus(x):
    for i in range(x,len(main)-1):
        if main[i]<0:
            return main[i]
    return 0
def findminus_plus(x):
    for i in range(x-1,-1,-1):
        if main[i]>=0:
            return main[i]
    return -1
def findminus_minus(x):
    for i in range(x-1,-1,-1):
        if main[i]<0:
            return main[i]
    return 0
    
if num==k:
    for i in main:
        result*=i
elif sorted(main)[len(sorted(main))-1]<0:
    if (k%2)==0:
        for i in range(k):
            result*=main[i]
    else:
        for i in range(len(main)-1,len(main)-1-k,-1):
            result*=main[i]
else:
    for i in range(k):
        result*=main[i]
    if result<0:
        if findplus_plus(k)==-1:
            plusplus=0
            minusminus=findminus_minus(k)*findplus_minus(k)
        else:
            plusplus=findplus_plus(k)*findminus_plus(k)
            if findplus_minus(k)==0 or findminus_plus(k)==-1:
                minusminus=0
            else:
                minusminus=findminus_plus(k)*findminus_minus(k)
        if plusplus>minusminus:
            result=int(result*findplus_plus(k)/findminus_minus(k))
        elif plusplus<=minusminus:
            result=int(result*findplus_minus(k)/findminus_plus(k))
print(result%(10**9+7))