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 Rust (1.42.0) (judge verdict: Wrong Answer)

use proconio::{input, fastout};

const MOD_UNIT: i64 = 1_000_000_007;

#[fastout]
fn main() {
    input! {
        n: usize,
        k: usize,
        mut a: [i64; n],
    }

    a.sort_by(|i, j| i.abs().cmp(j).reverse());

    let mut negative_cnt = 0;
    let mut last_positive_i: Option<usize> = None;
    let mut last_negative_i: Option<usize> = None;
    let mut outer_first_positive_i: Option<usize> = None;
    let mut outer_first_negative_i: Option<usize> = None;
    for i in 0..(a.len()) {
        if i < k {
            if a[i] < 0 {
                negative_cnt += 1;
                last_negative_i = Some(i);
            } else if a[i] > 0 {
                last_positive_i = Some(i);
            } else {
                last_negative_i = Some(0);
                last_positive_i = Some(0);
            }
        } else {
            if negative_cnt % 2 == 0 {
                break;
            }
            if a[i] < 0 {
                outer_first_negative_i = Some(i);
                if outer_first_positive_i != None {
                    break;
                }
            } else {
                outer_first_positive_i = Some(i);
                if outer_first_negative_i != None {
                    break;
                }
            }
        }
    }

    let mut res = 1;
    if negative_cnt % 2 == 0 || a.len() == k {
        for i in 0..k {
            res = (res * a[i]) % MOD_UNIT;
        }
    } else if last_positive_i == None {
        if outer_first_positive_i == None {
            for i in 0..k {
                res = (res * a[a.len() - i - 1]) % MOD_UNIT;
            }
        } else {
            for i in 0..k {
                if i == last_negative_i.unwrap() {
                    continue;
                }
                res = (res * a[i]) % MOD_UNIT;
            }
            res = (res * a[outer_first_positive_i.unwrap()]) % MOD_UNIT;
        }
    } else if last_negative_i == None {
        panic!("can not happen");
    } else {
        if outer_first_positive_i == None 
            || a[last_positive_i.unwrap()] * a[outer_first_positive_i.unwrap()] 
                < a[last_negative_i.unwrap()] * a[outer_first_negative_i.unwrap()] {
            for i in 0..k {
                if i == last_positive_i.unwrap() {
                    continue;
                }
                res = (res * a[i]) % MOD_UNIT;
            }
            res = (res * a[outer_first_negative_i.unwrap()]) % MOD_UNIT;
        } else {
            for i in 0..k {
                if i == last_negative_i.unwrap() {
                    continue;
                }
                res = (res * a[i]) % MOD_UNIT;
            }
            res = (res * a[outer_first_positive_i.unwrap()]) % MOD_UNIT;
        }
    }

    if res < 0 {
        res = MOD_UNIT + res;
    }

    println!("{}", res);
}