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: Wrong Answer)

n,k = map(int,input().split())
a = list(map(int,input().split()))
mod = 10**9 + 7
b_p = []
b_n = []
ab = []
for i in range(n):
    ab.append([abs(a[i]), a[i]])
    if a[i] >= 0:
        b_p.append(a[i])
    else:
        b_n.append(a[i])
b_p = sorted(b_p,reverse=True)
b_n = sorted(b_n)
ab.sort(key= lambda val : val[0])
ans = 1
i = 0
x = 0
y = 0
if k%2 == 1:
    if len(b_p) >= 1:
        ans *= b_p[0]
        x += 1
        i += 1
while i < k-1:
    i += 2
    if x < len(b_p)-1 and y < len(b_n)-1:
        if b_p[x]*b_p[x+1] > b_n[y]*b_n[y+1]:
            ans *= b_p[x]*b_p[x+1]
            ans %= mod
            x += 2
        else:
            ans *= b_n[y]*b_n[y+1]
            ans %= mod
            y += 2
    
    elif x < len(b_p)-1:
        ans *= b_p[x]*b_p[x+1]
        ans %= mod
        x += 2
    elif y < len(b_n)-1:
        ans *= b_n[y]*b_n[y+1]
        ans %= mod
        y += 2
    
if i != k:
    if 0 in b_p:
        ans = 0
    else:
        ans = 1
        for i in range(k):
            ans *= ab[i][1]
            ans %= mod
        
print(ans%mod)