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: Accepted)

import sys

mod = 10 ** 9 + 7

N, K = map(int,input().split())
A = list(map(int,input().split()))

A.sort(reverse = True)

if A[0] < 0 and K % 2 == 1:
    ans = 1
    for i in range(K):
        ans *= A[i]
        ans %= mod
    print(ans)
    sys.exit()

l = 0
r = N-1

ans = 1
if K % 2 == 1:
    ans *= A[0]
    l += 1

for _ in range(K // 2):
    if A[l] * A[l+1] > A[r] * A[r-1]:
        ans *= A[l] * A[l+1]
        ans %= mod
        l += 2
    else:
        ans *= A[r] * A[r-1]
        ans %= mod
        r -= 2

print(ans)