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: Accepted)

from collections import defaultdict
def prod(A,k,mod):
  ans = 1
  for i in range(k):
      ans *= A[i]
      ans %= mod
  return ans
def solve():
  N, K = map(int, input().split())
  A = list(map(int, input().split()))
  mod = 10**9+7
  ans = 1
  if K==N:
    return prod(A,N,mod)
  minus = len([a for a in A if a<0])
  if minus==N:
    if K%2==0:
      A.sort()
    else:
      A.sort(reverse=True)
    return prod(A,K,mod)
  if K==1:
    return max(A)
  A.sort(key=lambda x:-abs(x))
  if A[K]==0:
    return 0
  minus = len([a for a in A[:K] if a<0])
  flag = [1]*K+[0]*(N-K)
  d = defaultdict(lambda: -1)
  if minus%2==1:
    for i in range(K,N):
      if A[i]>=0:
        d['p2'] = i
        break
    for i in range(K,N):
      if A[i]<0:
        d['m2'] = i
        break
    for i in range(K-1,-1,-1):
      if A[i]>0:
        d['p1'] = i
        break
    for i in range(K-1,-1,-1):
      if A[i]<0:
        d['m1'] = i
        break
    if d['p2']==-1 or d['m1']==-1:
      flag[d['m2']],flag[d['p1']] = 1,0
    elif d['m2']==-1 or d['p1']==-1:
      flag[d['p2']],flag[d['m1']] = 1,0
    elif A[d['p2']]*A[d['p1']]>A[d['m1']]*A[d['m2']]:
        flag[d['p2']],flag[d['m1']] = 1,0
    else:
      flag[d['m2']],flag[d['p1']] = 1,0
    ans = 1
    for i in range(N):
      if flag[i]==1:
        ans *= A[i]
        ans %= mod
    return ans
  return prod(A,K,mod)
print(solve())