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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

n,k = map(int,input().split())
a = list(map(int,input().split()))
mod = 10**9 +7

a_plus = []
a_minus = []
cnt_0 = 0

for ai in a:
    if(ai==0):
        cnt_0 += 1
    elif(ai > 0):
        a_plus.append(ai)
    else:
        a_minus.append(ai)

a_plus.sort(reverse = True)
a_minus.sort()

cnt_p = len(a_plus)
cnt_m = len(a_minus)

if(cnt_p + cnt_m < k):
    print(0)
    exit()


if(cnt_m == n)&(k%2==1):
    ans = 1
    for i in range(k):
        ans *= a_minus[cnt_m - 1 - i]
        ans %= mod
    print(ans)
    exit()
elif(cnt_p == 0)&(k%2==1):
    print(0)
    exit()

p_ind = 0
m_ind = 0

ans = 1
if(k%2==1):
    ans = a_plus[0]
    p_ind = 1

for i in range(k//2):
    tmp_p = 0
    tmp_m = 0
    if(p_ind + 2 <= cnt_p ):
        tmp_p = a_plus[p_ind] * a_plus[p_ind+1]

    if(m_ind + 2 <= cnt_m ):
        tmp_m = a_minus[m_ind] * a_minus[m_ind+1]

    if(tmp_p > tmp_m):
        ans *= tmp_p
        p_ind += 2
    else:
        ans *= tmp_m
        m_ind += 2
    ans %= mod


ans %= mod
print(ans)