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)

import sys
input = sys.stdin.readline

N, K = [int(x) for x in input().split()]
A = [int(x) for x in input().split()]

s = [];  t = [];
for a in A:
    if a < 0:
        t.append(a)
    else:
        s.append(a)

P = 10 ** 9 + 7
# 非負にできるか判定
S = len(s)
T = len(t)
ok = False
if S > 0:
    if N == K:
        ok = (T % 2 == 0)
    else:
        ok = True
else:
    ok = (K % 2 == 0)

ans = 1
if not ok:
    A.sort(key = lambda x: abs(x))  # 絶対値小→大
    for i in range(K):
        ans = ans * A[i] % P
else:   # 非負にできる
    s.sort()    # 小→大
    t.sort(reverse = True)  # 絶対値小→大
    if K % 2 == 1:
        ans *= s.pop() # 一番大きい正の数を確保

    p = []
    while len(s) >= 2:
        x = s.pop()
        x = x * s.pop() % P
        p.append(x)

    while len(t) >= 2:
        x = t.pop()
        x = x * t.pop()
        p.append(x)

    p.sort(reverse = True)
    for i in range(K // 2):
        ans = ans * p[i] % P


print(ans)