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: Accepted)

import sys
input = sys.stdin.buffer.readline

def main():
    N, K = map(int,input().split())
    A = list(map(int,input().split()))
    A.sort()
    l, r = 0, N-1
    MOD = 10**9+7
    if K == N:
        ans = 1
        for num in A:
            ans *= num
            ans = (ans+MOD)%MOD
        print((ans+MOD)%MOD)
        exit()
    elif A[-1] < 0 and K%2 == 1:
        ans = 1
        for i in range(K):
            ans *= A[-i-1]
            ans = (ans+MOD)%MOD
        print(ans)
        exit()
    ans = 1
    if K%2 == 1:
        ans *= A[-1]
        r -= 1
    for _ in range(K//2):
        nl = A[l]*A[l+1]
        nr = A[r]*A[r-1]
        if nl > nr:
            ans *= nl
            l += 2
        else:
            ans *= nr
            r -= 2
        ans = (ans+MOD)%MOD
    print(ans)
    
if __name__ == "__main__":
    main()