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()))
m=10**9+7
ans=0
if n==k:
  ans=a[0]
  for i in range(1,n):
    ans=(ans*a[i])%m
else:
  a.sort()
  if a[n-1]<0:
    ans=a[n-1]
    for i in range(n-2,n-k-1,-1):
      ans=(ans*a[i])%m
  else:
    if k&1:
      ans=a[n-1]
      plus=n-2
      pluss=a[n-2]*a[n-3]
    else:
      ans=1
      plus=n-1
      pluss=a[n-1]*a[n-2]
    minus=0
    minuss=a[0]*a[1]
    for i in range(k//2):
      if minuss>=pluss:
        ans=(ans*(minuss%m))%m
        minus+=2
        minuss=a[minus]*a[minus+1]
      else:
        ans=(ans*(pluss%m))%m
        plus-=2
        pluss=a[plus]*a[plus-1]
print(ans)