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,=map(int, input().split())

ans=1
mod=10**9+7

a.sort()
if a[0]>=0:
    for i in range(n-1,n-k,-1):
        ans*=a[i]
        ans%=mod
    print(ans)
    exit()
if a[-1]<0:
    for i in range(n-1,n-k-1,-1):
        ans*=a[i]
        ans%=mod
    print(ans)
    exit()
l=0;r=n-1
while k:
    if k>=2:
        if a[l]*a[l+1]>a[r]*a[r-1]:
            ans*=a[l]*a[l+1]
            l+=2
        else:
            ans*=a[r]*a[r-1]
            r-=2
        k-=2
        ans%=mod
    else:
        if a[l]>a[r]:
            ans*=a[l]
        else:
            ans*=a[r]
        k-=1
print(ans)