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)

N, K = map(int, input().split())
A = list(map(int, input().split()))
MOD = 10 ** 9 + 7
p, m, ans = [], [], 1
for i in A:
    if i < 0:
        m.append(i)
    else:
        p.append(i)

m.sort(reverse=True)
p.sort()


if not len(p):
    for i in range(K):
        ans *= m[i]
        ans %= MOD

else:
    ispass = False
    tmp = len(p)
    for i in range(K):
        if ispass:
            ispass = False
            continue
        if K - i == 1:
            ans *= p[-1]
            ans %= MOD

        elif tmp < K - i - 1:
            ans *= -m[-1]
            ans %= MOD
            ans *= -m[-2]
            ans %= MOD
            m = m[0:-2]
            ispass = True

        else:
            if m[-1] * m[-2] > p[-1] * p[-2]:
                ans *= -m[-1]
                ans %= MOD
                ans *= -m[-2]
                ans %= MOD
                m = m[0:-2]
                isPass = True
            else:
                ans *= p[-1]
                ans %= MOD
                ans *= p[-2]
                ans %= MOD
                p = p[0:-2]
                isPass = True

print(ans)