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()))

A_p = [i for i in A if i >= 0]
A_n = [i for i in A if i < 0]
A_p.sort()
A_p.reverse()
A_n.sort()

ans = 1
p = 0
n = 0
mod = 10 ** 9 + 7
if K % 2 == 0:
    while K != 0:
        if len(A_p) >= 2 and len(A_n) >= 2:
            if A_p[p] * A_p[p+1] > A_n[n] * A_n[n+1]:
                ans = ans * A_p[p] * A_p[p+1] % mod
                p += 2
            else:
                ans = ans * A_n[n] * A_n[n+1] % mod
                n += 2
        elif len(A_p) >= 2:
            ans = ans * A_p[p] * A_p[p+1] % mod
            p += 2
        elif len(A_n) >= 2:
            ans = ans * A_n[n] * A_n[n+1] % mod
            n += 2
        K -= 2
elif len(A_p) > 0:
    while K != 0:
        if K >= 2:
            if len(A_p) >= 2 and len(A_n) >= 2:
                if A_p[p] * A_p[p+1] > A_n[n] * A_n[n+1]:
                    ans = ans * A_p[p] * A_p[p+1] % mod
                    p += 2
                else:
                    ans = ans * A_n[n] * A_n[n+1] % mod
                    n += 2
            elif len(A_p) >= 2:
                ans = ans * A_p[p] * A_p[p+1] % mod
                p += 2
            elif len(A_n) >= 2:
                ans = ans * A_n[n] * A_n[n+1] % mod
                n += 2
            K -= 2
        elif K == 1:
            ans = ans * A_p[p] % mod
            K -= 1
else:
    n = len(A_n) - 1
    while K != 0:
        ans = ans * A_n[n] % mod
        n -= 1
        K -= 1

print(ans)