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()))
A.sort()
z = 0
for i in range(0,N-1):
    if A[i]<0 and A[i+1]>0:
        P = A[i+1:][::-1]
        M = A[:i+1]
        break
    if A[N-1]<0:
        P = []
        M = A[:]
        break
    if A[0] >0:
        P=A[:]
        M=[]
MOD = 10**9+7

p = 0
m = 0
lp = None
lm = None
l = []
for i in range(K):
    if p>=len(P):
        l.append(M[m])
        lm = M[m]
        m+=1
    elif m>=len(M):
        l.append(P[p])
        lp = P[p]
        p+=1
    elif P[p] > -1*M[m]:
        l.append(P[p])
        lp = P[p]
        p+=1
    else:
        l.append(M[m])
        lm = M[m]
        m+=1
if m%2 == 0:
    ans = 1
    for i in range(K):
        ans = (ans*l[i])%MOD
    print(ans)
else:
    if p >= len(P):#+がもうない
        if lp == None:
            B = M[::-1]
            l = B[:K]
        MM = M[m]
        for i in range(0, K):
            if l[K-i-1] == lp:
                l[K-i-1] = MM
                break
    elif m >= len(M):#-がもうない
        MP = M[m]
        for i in range(0, K):
            if l[K-i-1] == lm:
                l[K-i-1] = MP
                break
    elif P[p] > -1*M[m]:
        MP = P[p]
        MM = M[m]
        if -1*lm < lp:#(i)
            if MP * lm > MM * lp:
                for i in range(0, K):
                    if l[K-i-1] == lm:
                        l[K-i-1] = MP
                        break
            else:
                for i in range(0, K):
                    if l[K-i-1] == lp:
                        l[K-i-1] = MM
                        break
        else:#(ii)
            for i in range(0, K):
                    if l[K-i-1] == lm:
                        l[K-i-1] = MP
                        break
    elif P[p] < -1*M[m]:
        MP = P[p]
        MM = M[m]
        if -1*lm < lp:#(i)
            for i in range(0, K):
                    if l[K-i-1] == lm:
                        l[K-i-1] = MP
                        break
            if MP * lm > MM * lp:
                for i in range(0, K):
                    if l[K-i-1] == lm:
                        l[K-i-1] = MP
                        break
            else:
                for i in range(0, K):
                    if l[K-i-1] == lp:
                        l[K-i-1] = MM
                        break
        else:#(ii)
            if MP * lm > MM * lp:
                for i in range(0, K):
                    if l[K-i-1] == lm:
                        l[K-i-1] = MP
                        break
            else:
                for i in range(0, K):
                    if l[K-i-1] == lp:
                        l[K-i-1] = MM
                        break
    ans = 1
    for i in range(K):
        ans = (ans*l[i])%MOD
    print(ans)