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()))
m = 10**9+7
p = []
q = []
r = []
for i in range(N):
    if A[i] > 0:
        p.append(A[i])
    elif A[i] < 0:
        q.append(A[i])
    else:
        r.append(A[i])
p.sort()
q.sort()
P = len(p)
Q = len(q)
if P+Q < K:
    print(0)
    exit()
if P > 0:
    if P+Q == K:
        ans = 1
        for i in range(P):
            ans = ans * p[i] % m
        for i in range(Q):
            ans = ans * q[i] % m
        print(ans)
    else:
        i = K
        j = 0
        while i > P:
            i -= 2
            j += 2
            
        while i >= 1 and j < Q-1:
            if p[P-i]*p[P-i+1] < q[Q-j-1]*q[Q-j-2]:
                if i-2 >= 1:
                    i -= 2
                j += 2
            else:
                break
        ans = 1
        for k in range(max(0,i)):
            ans = ans * p[P-k-1] % m
        for l in range(min(Q,j)):
            ans = ans * q[Q-l-1] % m
        print(ans)
else:
    if K % 2 == 0:
        if Q >= K:
            ans = 1
            for i in range(K):
                ans = ans * q[Q-1-i] % m
            print(ans)
        else:
            print(0)
    else:
        if len(r) > 0:
            print(0)
        else:
            ans = 1
            for i in range(K):
                ans = ans * q[Q-1-i] % m
            print(ans)