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: Accepted)

n,k=map(int,input().split())
a=list(map(int,input().split()))
a.sort(key=lambda x: -abs(x))
mod=10**9+7
p=1
mm=0
for i in range(k):
    if a[i]<0:
        mm+=1
    p*=a[i]
    p%=mod
if n==k or mm%2==0:
    print(p)
    exit()
    
m=0
for i in a:
    if i<=0:
        m+=1
if m==n:
    p=1
    for i in range(k):
        p*=a[n-i-1]
        p%=mod
    print(p)
    exit()
b1=[]
b2=[]
for i in range(k):
    if len(b1)==0 and a[k-1-i]>=0:
        b1.append(a[k-1-i])
    if len(b2)==0 and a[k-1-i]<0:
        b2.append(a[k-1-i])
for i in range(n-k):
    if len(b1)==1 and a[k+i]<0:
        b1.append(a[k+i])
    if len(b2)==1 and a[k+i]>=0:
        b2.append(a[k+i])
f=0
if len(b1)==len(b2)==2:
    if b1[1]*b2[0]>=b1[0]*b2[1]:
        f=1
    else:
        f=2
elif len(b2)<2:
    f=1
else:
    f=2

if f==1:
    p*=b1[1]*pow(b1[0],mod-2,mod)
    print(p%mod)
    exit()
else:
    p*=b2[1]*pow(b2[0],mod-2,mod)
    print(p%mod)
    exit()