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)

mod = 1000000007
N, K = list(map(int, input().split()))
A = list(map(int, input().split()))
A.sort()
ans = 1
# 負になってしまう時
if A[-1] < 0 and K%2 == 1:
    for i in range(K):
        ans = ans * (A[-i-1]%mod) % mod
else:
    n = 0
    p = -1
    # Kが奇数の時、正の候補の最大値をあらかじめ消費しておき、偶数の時と同様に処理できるようにする。
    if K%2 == 1:
        ans = ans * (A[p]%mod) % mod
        p -= 1
    # 正/負の候補から２つずつ消費していく
    for _ in range(K//2):
        if A[n]*A[n+1] > A[p]*A[p-1]:
            ans = ans * (A[n]%mod) % mod
            ans = ans * (A[n+1]%mod) % mod
            n += 2
        else:
            ans = ans * (A[p]%mod) % mod
            ans = ans * (A[p-1]%mod) % mod
            p -= 2        

print(ans)