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)

MOD = 10**9 + 7


class modint():
    def __init__(self, value):
        self.value = value % MOD

    def __int__(self):
        return int(self.value)

    def __float__(self):
        return float(self.value)

    def __str__(self):
        return str(self.value)

    def __repr__(self):
        return str(self.value)

    def __add__(self, other):
        return (modint(self.value + other.value) if isinstance(other, modint)
                else modint(self.value + other))

    def __sub__(self, other):
        return (modint(self.value - other.value) if isinstance(other, modint)
                else modint(self.value - other))

    def __mul__(self, other):
        return (modint(self.value * other.value) if isinstance(other, modint)
                else modint(self.value * other))

    def __truediv__(self, other):
        return (modint(self.value * pow(other.value, MOD - 2, MOD))
                if isinstance(other, modint)
                else modint(self.value * pow(other, MOD - 2, MOD)))

    def __pow__(self, other):
        return (modint(pow(self.value, other.value, MOD))
                if isinstance(other, modint)
                else modint(pow(self.value, other, MOD)))

    def __eq__(self, other):
        return (self.value == other.value if isinstance(other, modint)
                else self.value == (other % MOD))

    def __ne__(self, other):
        return (self.value == other.value if isinstance(other, modint)
                else self.value == (other % MOD))

    def __radd__(self, other):
        return (modint(other.value + self.value) if isinstance(other, modint)
                else modint(other + self.value))

    def __rsub__(self, other):
        return (modint(other.value - self.value) if isinstance(other, modint)
                else modint(other - self.value))

    def __rmul__(self, other):
        return (modint(other.value * self.value) if isinstance(other, modint)
                else modint(other * self.value))

    def __rtruediv__(self, other):
        return (modint(other.value * pow(self.value, MOD - 2, MOD))
                if isinstance(other, modint)
                else modint(other * pow(self.value, MOD - 2, MOD)))

    def __rpow__(self, other):
        return (modint(pow(other.value, self.value, MOD))
                if isinstance(other, modint)
                else modint(pow(other, self.value, MOD)))

    def modinv(self):
        return modint(pow(self.value, MOD - 2, MOD))


def main():
    from collections import Counter
    N, K = (int(i) for i in input().split())
    A = [int(i) for i in input().split()]
    posi = [a for a in A if a > 0]
    nega = [a for a in A if a < 0]
    posi.sort(reverse=True)
    nega.sort(reverse=True)
    A.sort(reverse=True, key=abs)
    if len(posi) + len(nega) < K:
        # 0を含まなければいけないとき
        return print(0)

    ans = modint(1)
    if K % 2 == 1 and len(posi) < K:
        # 結果が負数
        # 絶対値が小さいやつをK個取ってくる
        A.sort(key=abs)
        for a in A[:K]:
            ans *= a
    else:
        # 結果が正になるように注意しなければいけない
        # skipしてかけるものがなくなったらこわい
        # 負数がK以下の奇数個しかないとハマる
        if sum(a < 0 for a in A[:K]) % 2 == 0:
            for a in A[:K]:
                ans *= a
        else:
            ans1 = []  # 正を取り除く
            ans2 = []  # 負を取り除く
            posi = [a for a in A[:K] if a > 0]
            nega = [a for a in A[:K] if a < 0]
            p_remove = False
            for a in A[:K][::-1]:
                if a > 0 and not p_remove:
                    p_remove = True
                    continue
                ans1.append(a)
            n_remove = False
            for a in A[:K][::-1]:
                if a < 0 and not n_remove:
                    n_remove = True
                    continue
                ans2.append(a)
            mul1 = 0  # 一番大きい正
            mul2 = 0  # 　一番大きい負
            for a in A[K:]:
                if mul1 == 0 and a > 0:
                    mul1 = a
                if mul2 == 0 and a < 0:
                    mul2 = a
                if mul1 != 0 and mul2 != 0:
                    break
            ans1.append(mul2)
            ans2.append(mul1)
            s1 = sum(abs(a) for a in ans1)
            s2 = sum(abs(a) for a in ans2)

            if len(posi) == 0 or mul2 == 0:
                for a in ans2:
                    ans *= a
            elif len(nega) == 0 or mul1 == 0:
                for a in ans1:
                    ans *= a
            else:
                if s1 > s2:
                    for a in ans1:
                        ans *= a
                else:
                    for a in ans2:
                        ans *= a
    print(ans)


if __name__ == '__main__':
    main()