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: Runtime Error)

n, k = map(int, input().split())
a = list(map(int, input().split()))

a.sort(reverse=True, key=lambda x:abs(x))
cnt = 0
im = 0
ip = 0
cp = 0
mod = 10 ** 9 + 7

for i, ai in enumerate(a):
    if i < k:
        if ai < 0:
            im = i
            cnt += 1
        if ai > 0:
            ip = i
    if ai > 0:
        cp += 1

ans = 1
f = 0

# print(a)
if cnt % 2:
    if cp == 0:
        a.sort(reverse=True)
        for i, ai in enumerate(a):
            if i == k:
                break
            ans *= ai
            ans %= mod
        print(1/0)
        print(ans)
    else:
        ans = 1
        cnt = 0
        f = 0
        for i, ai in enumerate(a):
            if cnt == k:
                f = 2
                break
            if i == im:
                f = 1
                continue
            if f == 1 and ai <= 0:
                continue
            ans *= abs(ai)
            ans %= mod
            # print(i, ai)
            cnt += 1
        if f == 2:
            print(ans)
        else:
            ans = 1
            cnt = 0
            f = 0
            for i, ai in enumerate(a):
                if cnt == k:
                    f = 2
                    break
                if i == ip:
                    f = 1
                    continue
                if f == 1 and ai >= 0:
                    continue
                ans *= abs(ai)
                ans %= mod
                # print(i, ai)
                cnt += 1
            if f == 2:
                print(ans)
            else:
                ans = 1
                a.sort(reverse=True)
                for i, ai in enumerate(a):
                    if i == k:
                        break
                    ans *= ai
                    ans %= mod
                print(ans)

else:
    for i, ai in enumerate(a):
        if i == k:
            break
        ans *= abs(ai)
        ans %= mod
    print(ans)