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
n,k=map(int,input().split())
a = list(map(int,input().split()))
plus = sorted([i for i in a if i > 0],reverse=True)
minus = sorted([i for i in a if i < 0])
b = []
p = 0
m = 0
MOD = 10**9 + 7

while(True):
    if(p == len(plus)):
        for i in range(k-p-m):
            b.append(minus[i+m])
        break
    if(m == len(minus)):
        for i in range(k-p-m):
            b.append(plus[i+p])
        break
    if(plus[p] >= -minus[m]):
        b.append(plus[p])
        p += 1
    else:
        b.append(minus[m])
        m += 1
    if(p+m == k):
        if(m % 2 == 1):
            if(minus[m]*minus[m-1] > plus[p]*plus[p-1]):
                b[b.index(plus[p-1])] = minus[m]
            else:
                b[b.index(minus[m-1])] = plus[p]
        break
if(len([i for i in b if i<0]) %2 != 0):
    if(0 in a):
        print(0)
        sys.exit()
    else:
        ans = 1
        for i in a:
            if(i < 0):
                i *= -1
        a = sorted(a,reverse=True)
        print(a)
        for i in range(k):
            ans = ans*a[i] % MOD
        ans = -((-1 * ans) % -MOD)
        print(ans)
        sys.exit()
ans = 1
for i in b:
    ans = ans*i % MOD
print(ans)