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)

#!/usr/bin/env python3

import sys
import math
from bisect import bisect_right as br
from bisect import bisect_left as bl
sys.setrecursionlimit(2147483647)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

n, k = LI()
a = LI()
a.sort(key = lambda x:abs(x), reverse = True)
ans = 1
p = 0
m = 0
plus = []
minus = []
f = 0
for i in range(n):
    if a[i] >= 0:
        plus.append(a[i])
        p += 1
        if i < k:
            ans *= a[i]
            ans %= mod
    else:
        minus.append(a[i])
        m += 1
        if i < k:
            f ^= 1
            ans *= -a[i]
            ans %= mod
if f:
    ans = -ans
if ans < 0:
    if k == n:
        print(ans)
    elif p == 0:
        a.sort(key = lambda x:abs(x))
        ans = 1
        for i in range(k):
            ans *= -a[i]
            ans %= mod
        if k % 2:
            ans = -ans
        print(ans % mod)
    else:
        ans1 = ans // minus[-1]
        f1 = 0
        f2 = 0
        for i in range(k, n):
            if a[i] >= 0:
                ans1 *= a[i]
                f1 = 1
                break
        ans2 = ans // plus[-1]
        ans2 = -ans2
        for i in range(k, n):
            if a[i] < 0:
                ans2 *= -a[i]
                f2 = 1
                break
        if f1 and f2:
            print(max(ans1, ans2) % mod)
        elif f1:
            print(ans1 % mod)
        else:
            print(ans2 % mod)
else:
    print(ans)