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)

MOD = 10**9 + 7

def prod(a):
    res = 1
    for x in a:
        res = (res * x) % MOD
    return res

def solve(n, k, a):
    if k == 1:
        return max(a)
    elif k == n:
        return prod(a)
    elif max(a) < 0:
        a = sorted(a, reverse=True)
        return prod(a[:k])
    else:
        a = sorted(a, key=lambda x: -abs(x))
        num_negative = len(list(filter(lambda x: x < 0, a[:k])))
        if num_negative % 2 == 0:
            return prod(a[:k])
        else:
            i1, j1 = None, None
            for i in range(k):
                if a[i] < 0:
                    i1 = i
            for j in range(k,n):
                if a[j] >= 0:
                    j1 = j
                    break
            i2, j2 = None, None
            for i in range(k):
                if a[i] >= 0:
                    i2 = i
            for j in range(k, n):
                if a[j] < 0:
                    j2 = j
                    break
            if ((i1 is None) or (j1 is None)) and ((i2 is None) or (j2 is None)):
                return prod(a[:k])
            elif (i1 is None) or (j1 is None):
                return prod(a[:i2] + a[i2+1:k] + [a[j2]])
            elif (i2 is None) or (j2 is None):
                return prod(a[:i1] + a[i1+1:k] + [a[j1]])
            elif abs(a[j1] * a[i2]) > abs(a[i1] * b[j2]):
                return prod(a[:i1] + a[i1+1:k] + [a[j1]])
            else:
                return prod(a[:i2] + a[i2+1:k] + [a[j2]])

n, k = map(int, input().split())
a = list(map(int, input().split()))
print(solve(n, k, a))