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)

# -*- coding: utf-8 -*-
"""
Created on Sun Jul  5 21:33:15 2020

"""

N, K = map(int,input().split())
A = list(map(int, input().split())) 
A = sorted(A, key=abs, reverse=True)
mod = 10**9+7
ans = 1
lp = 10**6
lm = 10**6
lpflag = 0
lmflag = 0
rp = 10**6
rm = 10**6
rpflag = 0
rmflag = 0
ans1 = 0
ans2 = 0
minus = 0
flag0 = 0
for i in range(K):
    if A[i] < 0:
        minus = (minus+1)%2
    ans = ans * A[i] % mod
if not minus:
    print(ans)
else:
    for i in range(K-1,-1,-1):
        if lp < 10**6 and lm < 10**6:
            break
        if A[i] > 0 and lpflag == 0:
            lpflag = 1
            lp = i
        elif A[i] < 0 and lmflag == 0:
            lmflag = 1
            lm = i
    for i in range(K,N):
        if rp < 10**6 and rm < 10**6:
            break
        if A[i] > 0 and rpflag == 0:
            rpflag = 1
            rp = i
        elif A[i] < 0 and rmflag == 0:
            rmflag = 1
            rm = i
        elif A[i] == 0:
            flag0 = 1
    if lpflag*rmflag == 1:
        ans = 1
        for i in range(K):
            if not i == lp:
                ans = ans * A[i] % mod
        ans = ans * A[rm] % mod
        ans1 = ans
    if lmflag*rpflag == 1:
        ans = 1
        for i in range(K):
            if not i == lm:
                ans = ans * A[i] % mod
        ans = ans * A[rp] % mod    
        ans2 = ans
    if lpflag*rmflag == 0 and lmflag*rpflag == 0:
        ans = 1
        for i in range(N-1,N-1-K,-1):
            ans = ans * A[i] % mod
        if flag0:
            print(0)
        else:
            print(ans)

    else:
        if ans1 > 0 and ans2 > 0:
            if abs(A[rm]/A[lp]) > abs(A[rp]/A[lm]):
                print(ans1)
            else:
                print(ans2)
        else:
            print(max(ans1,ans2))