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()))

mainasu=[]
purasu=[]
for aa in a:
    if aa>=0:
        purasu.append(aa)
    else:
        mainasu.append(aa*(-1))



mod=10**9+7

#回答がプラスになるケース
if (k<n and len(purasu)>0) or (k<n and k%2==0) or (k==n and len(mainasu)%2==0):
    p_pos=0
    m_pos=0
    mainasu.sort(reverse=True)
    purasu.sort(reverse=True)
    ans=1
    cnt=0
    while cnt<k:
        ans=ans%mod
        #どっちからでも選べる
        if p_pos<len(purasu) and m_pos < len(mainasu):
            #もし最後から2つ目
            if cnt==k-2:
                if p_pos==len(purasu)-1:
                    ans*=mainasu[m_pos]%mod
                    m_pos+=1
                    ans*=mainasu[m_pos]%mod
                    m_pos+=1
                    cnt+=2
                elif purasu[p_pos]*purasu[p_pos+1]>mainasu[m_pos]*mainasu[m_pos+1]:
                    ans*=purasu[p_pos]%mod
                    p_pos+=1
                    ans*=purasu[p_pos]%mod
                    p_pos+=1
                    cnt+=2
                else:
                    ans*=mainasu[m_pos]%mod
                    m_pos+=1
                    ans*=mainasu[m_pos]%mod
                    m_pos+=1
                    cnt+=2
            else:
                if purasu[p_pos]>mainasu[m_pos+1]:
                    ans=ans*purasu[p_pos]%mod
                    cnt+=1
                    p_pos+=1
                else:
                    ans*=mainasu[m_pos]%mod
                    m_pos+=1
                    ans*=mainasu[m_pos]%mod
                    m_pos+=1
                    cnt+=2
        elif p_pos<len(purasu):
            ans=ans*purasu[p_pos]%mod
            cnt+=1
            p_pos+=1
        else:
            ans*=mainasu[m_pos]%mod
            m_pos+=1
            ans*=mainasu[m_pos]%mod
            m_pos+=1
            cnt+=2
    print(ans%mod)









#回答がマイナスになるケース
else:
    pm=purasu+mainasu
    pm.sort()
    ans=1
    for i in range(k):
        ans=ans*pm[i]%mod
        ans=ans%mod
    #print(-1*ans)
    print((-1*ans)%mod)