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)

# from itertools import accumulate as acc

MOD = 10**9 + 7

N, K = map(int, input().split())
A = list(map(int, input().split()))

A.sort()

plus_list = []
minus_list = []

zero_count = 0
for a in A:
    # print(a)
    if a > 0:
        plus_list.append(a)
    elif a < 0:
        minus_list.append(a)
    else:
        zero_count += 1

plus_list.sort()
minus_list.sort()

def solve():
    plus_list_reverse_acc = [1]
    for a in plus_list[::-1]:
        plus_list_reverse_acc.append(
            (plus_list_reverse_acc[-1] * a) % MOD
        )
    minus_list_acc = [1]
    for a in minus_list:
        minus_list_acc.append(
            (minus_list_acc[-1] * a) % MOD
        )
    # print(plus_list_reverse_acc, minus_list_acc)
    r = -(10**18)
    for minus_count in range(0, K+1, 2):
        if minus_count > len(minus_list):
            continue
        plus_count = K-minus_count
        if plus_count > len(plus_list):
            continue
        x = (minus_list_acc[minus_count] * plus_list_reverse_acc[plus_count]) % MOD
        r = max(r, x)
    return r

if plus_list and (not minus_list):
    # print("plus")
    if len(plus_list) < K:
        r = 0
    else:
        r = 1
        for a in plus_list[-K:]:
            # print(r*a)
            r = (r * a) % MOD
        # print(A[-K:], r)
elif (not plus_list) and minus_list:
    # print("minus")
    if K%2 == 1:
        if zero_count:
            r = 0
        else:
            r = 1
            for a in minus_list[-K:]:
                r = (r * a) % MOD
    else:
        if len(minus_list) < K:
            r = 0
        else:
            r = 1
            for a in minus_list[:K]:
                r = (r * a) % MOD
elif (not plus_list) and (not minus_list):
    # print("zero")
    r = 0
else:
    # print("plus minus zero")
    # 2要素以上
    if K == N:
        r = (zero_count == 0)
        for a in plus_list:
            r = (r * a) % MOD
        for a in minus_list:
            r = (r * a) % MOD
    else:
        # K <= N-1:
        # print(zero_count)
        if zero_count:
            # 3要素以上
            if K > N-zero_count:
                r = 0
            elif K == N-zero_count:
                if len(minus_list)%2 == 1:
                    r = 0
                else:
                    r = 1
                    for a in plus_list:
                        r = (r * a) % MOD
                    for a in minus_list:
                        r = (r * a) % MOD
            else:
                r = solve()
        else:
            # 2要素以上 
            r = solve()

print(r)