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: Wrong Answer)

import sys

MOD = 10**9+7

N,K = map(int, input().split())
A = [[abs(int(x)),1 if int(x)<0 else 0] for x in input().split()]
A.sort(key=lambda x: x[0],reverse=True)
prod = 1
pn = 0
lastn = -1
lastp = -1


for i in range(K):
    if A[i][1] == 1: lastn = i
    else: lastp = i
    pn = (pn + A[i][1]) % 2


if pn == 0:
    if K == N and 0 in A:
        print(0)
        sys.exit()
    for i in range(K):
        prod = prod * A[i][0] % MOD
    print(prod)
    sys.exit()

elif pn == 1:
    if K == N:
        if 0 in A:
            print(0)
            sys.exit(0)
        for i in range(N):
            prod = prod * A[i][0] % MOD
            prod = prod * (-1) % MOD
        print(prod)
        sys.exit()
    indp = K
    indn = K
    while indp < N and A[indp][1] == 1:
        indp += 1
    while indn < N and A[indn][1] == 0:
        indn += 1
    if lastp == -1 and indp == N:
        if K % 2 == 0:
            for i in range(K):
                prod = prod * A[i][0] % MOD
        elif K % 2 == 1:
            for i in range(K):
                B = list(reversed(A))
                prod = prod * B[i][0] % MOD
                prod = prod * (-1) % MOD
    elif indp == N:
        for i in range(K):
            if i == lastp:
                prod = prod * A[indn][0] % MOD
            else:
                prod = prod * A[i][0] % MOD
    elif indn == N:
        for i in range(K):
            if i == lastn:
                prod = prod * A[indp][0] % MOD
            else:
                prod = prod * A[i][0] % MOD
    else:
        prod1 = 1
        prod2 = 1
        for i in range(K):
            if i == lastn:
                prod1 = prod1 * A[indp][0] % MOD
                prod2 = prod2 * A[i][0] % MOD
            elif i == lastp:
                prod1 = prod1 * A[i][0] % MOD
                prod2 = prod2 * A[indn][0] % MOD
            else:
                prod1 = prod1 * A[i][0] % MOD
                prod2 = prod2 * A[i][0] % MOD
        prod = max(prod1,prod2)
    print(prod)