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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

n,k = map(int,input().split())
a = list(map(int,input().split()))
b=[]
for i in a:
    if i>0:
        m=1
    elif i==0:
        m=0
    else:
        m=-1
    b.append([abs(i),m])

b.sort(key=lambda x: x[0], reverse=True)

mod=10**9+7
ans=1
judge=1
seisaisyou=0
seisaidai=0
husaisyou=0
husaidai=0

for i in range(k):
    ans*=b[i][0]%mod
    judge*=b[i][1]
if judge>0:
    print(ans)
if judge<=0:
    
    for j in range(k-1,-1,-1):
        if b[i][1]==1:
            ss=b[i][0]#正の最小
            seisaisyou=1
            break
            
    for j in range(k-1,-1,-1):
        if b[i][1]==-1:
            hs=b[i][0]#負の最小
            husaisyou=1
            break
        
    
    #正の最小と　範囲外の負の最大を交換する
    for j in range(k,n):
        if b[i][1]==-1:
            h=b[i][0]#負の最大
            husaidai=1
            break
    
    #負の最小と　範囲外の正の最大を交換する
    for j in range(k,n):
        if b[i][1]==1:
            s=b[i][0]#正の最大
            seisaidai=1
            break
    
    if husaidai==1and seisaisyou==1:
        pre1=ans*h/ss
    if seisaidai==1and husaisyou==1:
        pre2=ans*s/hs
    if (husaidai==1and seisaisyou==1)or (seisaidai==1and husaisyou==1):
        ans=max(pre1,pre2)
        print(ans%mod)
    else:
        ans=1
        for i in range(n-1,n-k-1,-1):
            ans*=b[i][0]%mod
        print(mod-1*ans)