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: Runtime Error)

n,k=map(int, input().split())
a = list(map(int, input().split()))
mod=10**9+7
if n==k:
    ans=1
    for i in range(k):
        ans*=a[i]
        ans%=mod
    print(ans)
    exit()
minus=[i for i in a if i<0]
plus=[i for i in a if i>=0]
from collections import deque
minus=deque(sorted(minus))
plus=deque(sorted(plus,reverse=True))

n_minus=len(minus)
n_plus=len(plus)

if n_minus==n:
    ans=1
    if k%2==0:
        for i in range(k):
            ans*=minus.popleft()
            ans%=mod
        print(ans)
        exit()
    else:
        for i in range(k):
            ans*=minus.pop()
            ans%=mod
        print(ans)
        exit()

cnt_minus=0
cand=deque([])
for i in range(k):
    if not plus or abs(minus[0])>abs(plus[0]):
        cand.append(minus.popleft())
        cnt_minus+=1
    elif not minus or abs(minus[0])<abs(plus[0]):
        cand.append(plus.popleft())
    else:
        if cnt_minus%2==1:
            cand.append(minus.popleft())
            cnt_minus+=1
        else:
            cand.append(plus.popleft())

if cnt_minus%2==0:
    ans=1
    for i in range(k):
        ans*=cand[i]
        ans%=mod
    print(ans)
    exit()

tmpm,tmpp=None,None

for i in range(k-1,-1,-1):
    if cand[i]<0 and tmpm==None:
        tmpm=cand[i]
    elif cand[i]>=0 and tmpp==None:
        tmpp=cand[i]

cand1,cand2=None,None
if tmpm!=None and plus:
    cand1=plus[0]/abs(tmpm)
if tmpp!=None and minus:
    cand2=minus[0]/abs(tmpp)

if (cand1!=None and cand2==None) or cand1>=cand2:
    ans=1
    flg=True
    for i in range(k):
        if flg and cand[i]==tmpm:
            flg=False
            continue
        ans*=cand[i]
        ans%=mod
    print(ans*plus[0]%mod)
    exit()
elif (cand1==None and cand2!=None) or cand1<cand2:
    ans=1
    flg=True
    for i in range(k):
        if flg and cand[i]==tmpp:
            flg=False
            continue
        ans*=cand[i]
        ans%=mod
    print(ans*minus[0]%mod)
    exit()