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: Runtime Error)

N, K = list(map(int, input().split()))
A = list(map(int, input().split()))
MOD = 10 ** 9 + 7

if N - A.count(0) < K:
    print(0)
    exit(0)

plus = []
minus = []
for a in A:
    if a >= 0:
        plus.append(a)
    else:
        minus.append(a)


ans = 1
if K % 2 == 1 and len(plus) == 0:
    minus.sort(reverse=True)
    for i in range(K):
        ans *= minus[i]
        ans %= MOD
    print(ans)
    exit(0)

plus.sort(reverse=True)
minus.sort()

i = 0
j = 0

if K % 2 == 1 and len(plus) > 0:
    ans = plus[0]
    K -= 1
    plus = plus[1:]

for _ in range(K//2):
    if i+1 >= len(plus):
        ans *= (minus[j] * minus[j+1])
        ans %= MOD
        j += 2
        continue
    elif j+1 >= len(minus):
        ans *= (plus[i] * plus[i+1])
        ans %= MOD
        i += 2
        continue

    a = plus[i] * plus[i+1]
    b = minus[j] * minus[j+1]
    if a > b:
        ans *= a
        i += 2
    else:
        ans *= b
        j += 2
    ans %= MOD

print(ans)