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)

import sys
INF = 1 << 60
MOD = 10**9 + 7 # 998244353
sys.setrecursionlimit(2147483647)
input = lambda:sys.stdin.readline().rstrip()
mul = lambda x, y : x * y % MOD
from functools import reduce
def resolve():
    n, k = map(int, input().split())
    A = list(map(int, input().split()))
    A.sort(key = abs, reverse = 1)

    if all(a < 0 for a in A) or n == k:
        if k & 1:
            print(reduce(mul, A[-k:]))
        else:
            print(reduce(mul, A[:k]))
        return

    pos = []
    neg = []
    for a in A:
        if a >= 0:
            pos.append(a)
        else:
            neg.append(-a)

    pos.reverse()
    neg.reverse()
    ans = 1
    if k & 1:
        ans *= pos.pop()
        k -= 1

    for _ in range(k // 2):
        if len(pos) >= 2 and len(neg) >= 2:
            a, b = pos[-2:]
            c, d = neg[-2:]
            if a * b >= c * d:
                ans *= pos.pop()
                ans *= pos.pop()
                ans %= MOD
            else:
                ans *= neg.pop()
                ans *= neg.pop()
                ans %= MOD
        elif len(pos) >= 2:
            ans *= pos.pop()
            ans *= pos.pop()
            ans %= MOD
        elif len(neg) >= 2:
            ans *= neg.pop()
            ans *= neg.pop()
            ans %= MOD
    print(ans)
resolve()