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: Runtime Error)

import sys
sys.setrecursionlimit(10 ** 8)
MOD = 10 ** 9 + 7

def Z(): return int(input())
def ZZ(): return [int(_) for _ in input().split()]

def main():
    N, K = ZZ()
    A = ZZ()
    p = []
    z = []
    m = []
    for a in A:
        if a > 0: p.append(a)
        elif a == 0: z.append(a)
        else: m.append(a)

    if len(p) == 0 and len(z) == 0 and K%2 == 1: #答えが負
        m = sort(m)[::-1]
        ans = 1
        for i in range(K):
            ans *= m[i]
            ans %= MOD
        print(ans)
        return
    else:
        if K - len(p) - len(m) > 0:
            print(0)
            return
        else:
            p.sort(reverse=True)
            m.sort()
            ans = 1
            itr = itrp = 0
            while K > 0:
                if itr+1 < len(m): c1 = (m[itr] * m[itr+1])
                else: c1 = 0
                if itrp+1 < len(p): c2 = (p[itrp] * p[itrp+1])
                else: c2 = 0

                if c1 >= c2 and K >= 2:
                    ans *= c1
                    ans %= MOD
                    itr += 2
                    K -= 2
                else:
                    ans *= p[itrp]
                    ans %= MOD
                    itrp += 1
                    K -= 1
            print(ans)

    return

if __name__ == '__main__':
    main()