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: Wrong Answer)

#!/usr/bin/env python3
import os
from sys import stdin, stdout

MOD = int(1e9+7)

def solve(tc):
    n, k = map(int, stdin.readline().split())
    seq = list(map(int, stdin.readline().split()))

    seq = sorted(seq, key=lambda x: abs(x), reverse=True)

    contain_zero = False
    last_plus = -1
    last_minus = -1
    mul_minus = False

    arr = []
    p = 0
    while p < n and len(arr) < k:
        if seq[p] == 0:
            contain_zero = True
            p += 1
            continue

        if seq[p] < 0:
            last_minus = len(arr)
            mul_minus ^= True
        elif seq[p] > 0:
            last_plus = len(arr)

        arr.append(seq[p])
        p += 1

    # should contain zeros
    if p == n and len(arr)<k:
        print(0)
        return

    # found maximal
    if not mul_minus:
        ans = 1
        for num in arr:
            ans *= num
            ans %= MOD
        print(ans)
        return

    first_plus = -1
    first_minus = -1
    while p < n:
        if seq[p]==0:
            contain_zero = True
            p += 1
            continue

        if seq[p] < 0:
            if first_minus < 0:
                first_minus = p
        elif seq[p] > 0:
            if first_plus < 0:
                first_plus = p
        p += 1
    
    if first_plus < 0:
        if first_minus < 0:
            print(0)
            return
        elif last_plus < 0:
            if contain_zero:
                print(0)
            else:
                ans = 1
                for i in range(n-1, n-k-1, -1):
                    ans *= seq[i]
                    ans %= MOD
                print(ans)
            return
        else:
            arr[last_plus] = seq[first_minus]
    elif first_minus < 0:
        arr[last_minus] = seq[first_plus]
    else:
        if seq[first_plus]*arr[last_plus] < seq[first_minus]*arr[last_minus]:
            arr[last_plus] = seq[first_minus]
        else:
            arr[last_minus] = seq[first_plus]

    ans = 1
    for num in arr:
        ans *= num
        ans %= MOD
    print(ans)


tcs = 1
tc = 1
while tc <= tcs:
    solve(tc)
    tc += 1