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)

def main():
    def solve():
        ret = 1
        for i in range(n):
            if L[i][2]:
                ret *= L[i][0]
                ret %= MOD
        return ret % MOD

    n, k = map(int, input().split())
    A = list(map(int, input().split()))
    MOD = 10 ** 9 + 7
    INF = float('inf')
    L = []
    p, m = 0, 0
    for a in A:
        if a < 0:
            m += 1
            L.append([abs(a), -1, False])
        else:
            L.append([a, 1, False])
    L = sorted(L, key= lambda x: x[0], reverse=True)
    pm = 1
    lp, lm = None, None
    for i in range(k):
        L[i][2] = True
        pm *= L[i][1]
        if L[i][1] >= 0:
            lp = i
        else:
            lm = i
    if pm >= 0:
        ans = solve()
    else:
        ans1, ans2 = -INF, -INF
        flag1, flag2 = 0, 0
        if lp:
            j = k
            while j < n:
                if L[j][1] < 0:
                    ans1 = L[j][0] / L[lp][0]
                    flag1 = 1
                    break
                j += 1
        if lm:
            l = k
            while j < n:
                if L[l][1] >= 0:
                    ans2 = L[l][0] / L[lm][0]
                    flag2 = 1
                    break
                j += 1
        if ans1 >= ans2 and flag1:
            L[lp][2] = False
            L[j][2] = True
        if ans2 >= ans1 and flag2:
            L[lm][2] = False
            L[l][2] = True
        ans = solve()
        if ans1 == ans2 == -INF:
            L = sorted(L, key=lambda x: x[0])
            ans = 1
            for i in range(k):
                ans *= L[i][0]
                ans %= MOD
            ans = -1 * ans
    print(ans % MOD)
main()