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: Accepted)

n,k = map(int,input().split())
A = list(map(int,input().split()))
mod = 10**9+7
plus = []
minus=[]
for i in A:
    if i>=0:
        plus.append(i)
    else:
        minus.append(i)
ok = False
if len(plus)>0:
    if n==k:
        ok = (len(minus)%2==0)
    else:
        ok = True
else:
    ok = (k%2==0)
ans = 1
if not ok:
    A.sort(key=abs)
    for i in range(k):
        ans *= A[i]
        ans %= mod
else:
    plus.sort()
    minus.sort(reverse=True)
    if k%2 == 1:
        ans *= plus.pop()
    P = []
    while len(plus) >= 2:
        P.append((plus.pop())*(plus.pop()))
    while len(minus) >= 2:
        P.append((minus.pop())*(minus.pop()))
    P.sort(reverse=True)
    for i in range(k//2):
        ans *= P[i]
        ans %= mod
print(ans)