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: Runtime Error)

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

if all(a<0 for a in A):
    A.sort()
    ans = 1
    for _ in range(K):
        ans *= A.pop()
        ans %= MOD
    print(ans)
    exit()

arr = []
for a in A:
    if a < 0:
        arr.append((-a,1))
    else:
        arr.append((a,0))

arr.sort()
pz = []
ng = []
ans = 1
for _ in range(K):
    v,s = arr.pop()
    if s:
        ng.append(v)
    else:
        pz.append(v)

for v in ng:
    ans *= v
    ans %= MOD
for v in pz:
    ans *= v
    ans %= MOD
if len(ng)%2 == 0:
    print(ans)
    exit()

b = pz[-1] if pz else None
c = ng[-1] if ng else None
a = d = None
while arr and (a is None or d is None):
    v,s = arr.pop()
    if s:
        if a is None:
            a = v
    else:
        if d is None:
            d = v

assert (a is not None and b is not None) or (c is not None and d is not None)

if a is None or b is None:
    ans *= c * pow(d,-1,MOD)
elif c is None or d is None:
    ans *= a * pow(b,-1,MOD)
else:
    if a*d > b*c:
        ans *= a * pow(b,-1,MOD)
    else:
        ans *= c * pow(d,-1,MOD)
ans %= MOD
print(ans)