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()))
B=sorted([(a,abs(a)) for a in A],key=lambda x:x[1],reverse=True)
R=10**9+7
P=1
minus=0
last_neg=-1
last_pos=-1
for i in range(K):
    if i!=0:
        P=(P*B[i-1][1]) %R
    if B[i][0]>0:
        last_pos=i
    else:
        minus+=1
        last_neg=i
if minus%2==1:
    first_neg=-1
    first_pos=-1
    count=[0,0]
    for i in range(K,N):
        if count[0]==0 and B[i][0]>0:
            first_pos=i
            count[0]=1
            if last_neg<last_pos:
                count[1]=1
                break
        elif count[1]==0 and B[i][0]<0:
            first_neg=i
            count[1]=1
            if last_pos<last_neg:
                count[0]=1
                break
        elif count==[1,1]:
            break
    if last_pos==-1 and first_pos==-1:
        P=1
        for i in range(K):
            P=(P*B[N-i-1][0]) %R
        print(P)
        exit()
    list_product=[]
    if first_neg!=-1:
        list_product.append((P*B[first_neg][1]) %R)
    if first_pos!=-1:
        list_product.append((P*B[first_pos][1]) %R)
    print(max(list_product))
else:
    print(P*B[K-1][1] %R)