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: Time Limit Exceeded)

import sys

sys.setrecursionlimit(10 ** 7)
# import bisect
# import numpy as np
# from collections import deque
from collections import deque
# map(int, sys.stdin.read().split())
import itertools
import heapq


def input():
    return sys.stdin.readline().rstrip()


def main():
    N, K = map(int, input().split())
    A = list(map(int, input().split()))
    mod = 10 ** 9 + 7
    A.sort()
    A = deque(A)
    #    print(A)
    A_minus = deque([s for s in A if s < 0])
    A_plus = deque([s for s in A if s >= 0])

    #    print(A_plus)
    #    print(A_minus)
    AA = []
    if N == K:
        ans = 1
        for l in range(N):
            ans *= A[l] 
            ans %=mod
        print(ans % mod)

    elif K % 2 == 0:
        while len(A_minus) >= 2:
            a1 = A_minus.popleft()
            a2 = A_minus.popleft()
            AA.append(-a1 * a2)

        while len(A_plus) >= 2:
            a1 = A_plus.pop()
            a2 = A_plus.pop()
            AA.append(-a1 * a2)
        ans = 1
        heapq.heapify(AA)
        for i in range(K // 2):
            ans *= (-1 * heapq.heappop(AA)) % mod
        print(ans % mod)

    elif len(A_plus) == 0:
        ans = 1
        for i in range(K):
            ans *= A_minus.pop() % mod
        print(ans % mod)

    else:
        ans = A_plus.pop()
        while len(A_minus) >= 2:
            a1 = A_minus.popleft()
            a2 = A_minus.popleft()
            AA.append(-a1 * a2)

        while len(A_plus) >= 2:
            a1 = A_plus.pop()
            a2 = A_plus.pop()
            AA.append(-a1 * a2)

        heapq.heapify(AA)
        for i in range(K // 2):
            ans *= (-1 * heapq.heappop(AA)) % mod
        print(ans % mod)


if __name__ == "__main__":
    main()