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)

def resolve():
    def addans(i, ans):
        return ans * i % mod
    import sys
    import bisect
    input = sys.stdin.readline
    mod = 10 ** 9 + 7
    inf = float("inf")
    n, k = map(int, input().split())
    a = sorted(list(map(int, input().split())))
    l = bisect.bisect_left(a, 0)
    r = bisect.bisect_right(a, 0)
    if n - k < r - l:
        print(0)
        return
    if r == n:
        ans = 1
        for i in range(k):
            ans = addans(a[-i - 1], ans)
        print(ans)
        return
    ans = 1
    minus = a[::-1]
    plus = a
    if k % 2 == 1:
        ans = plus.pop()
        k -= 1
    try:
        m = minus.pop() * minus.pop()
    except:
        m = -inf
    try:
        p = plus.pop() * plus.pop()
    except:
        p = -inf
    for _ in range(k // 2):
        if p >= m:
            ans = addans(p, ans)
            try:
                p = plus.pop() * plus.pop()
            except:
                p = -inf
        else:
            ans = addans(m, ans)
            try:
                m = minus.pop() * minus.pop()
            except:
                m = -inf
    print(ans)


if __name__ == '__main__':
    resolve()