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: Wrong Answer)

# WA
from itertools import accumulate
from collections import deque
import sys
input = sys.stdin.readline

N, K = [int(x) for x in input().split()]
A = [int(x) for x in input().split()]
A.sort(reverse = True, key = lambda x : abs(x))
Aneg = [1 if A[i] < 0 else 0 for i in range(len(A))]
cum = list(accumulate(Aneg)) + [0]
p = 10 ** 9 + 7

# que = deque(A)
ans = 1
if (cum[N - 1] == N and K % 2 == 1) or K == N:  # 絶対マイナス使わなくちゃいけない
    for i in range(N - 1, N - K - 1, -1):
        ans = ans * A[i] % p
    print(ans)
    sys.exit()

k = 0
neg = False
# avoid = 1
for i in range(N):
    if A[i] == 0:
        ans = 0
        break
    if k >= K: break
    if A[i] > 0:
        ans = ans * abs(A[i]) % p
        k += 1
    elif neg:
        ans = ans * abs(A[i]) % p
        k += 1
        neg = not neg
    else:
        if cum[N - 1] - cum[i - 1] < 2 or k + 2 > K:
            continue
        ans = ans * abs(A[i]) % p
        k += 1
        neg = not neg
if neg:
    ans = (-ans) % p
print(ans)