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;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::f64::consts::*;

#[allow(unused)]
const INF: usize = std::usize::MAX / 4;
#[allow(unused)]
const M: isize = 1000000007;

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

    let mut a_plus = vec![];
    let mut a_minus = vec![];
    let mut a_zero = 1;
    for &ai in &a {
        if ai > 0 {
            a_plus.push((ai, 1));
        } else if ai < 0 {
            a_minus.push(ai);
        } else {
            a_zero += 1;
        }
    }

    let np = a_plus.len();
    let nm = a_minus.len();

    if np + nm < k {
        println!("0");
        return;
    }

    a_minus.sort();

    for i in (0..nm).step_by(2) {
        if i + 1 < nm {
            a_plus.push((a_minus[i] * a_minus[i + 1], 2));
        }
    }

    a_plus.sort();
    a_plus.reverse();
    // eprintln!("{:?}", a_plus);
    // eprintln!("{:?}", a_minus);

    let mut count = 0;
    let mut result = 1;
    let mut last_minus = INF;
    let mut last_plus = INF;
    for i in 0..a_plus.len() {
        let (ai, c) = a_plus[i];
        if c == 2 {
            if count + c <= k {
                result = result * ai % M;
                count += c;
                last_minus = i;
            }
        } else {
            result = result * ai % M;
            count += c;
            last_plus = i;
        }
        if count == k {
            break;
        }
    }

    if count < k {
        eprintln!("less");
        count = 0;
        result = 1;
        for i in 0..a_plus.len() {
            let (ai, c) = a_plus[i];
            if c == 2 {
                if count + c <= k && i < last_minus {
                    result = result * ai % M;
                    count += c;
                }
            } else {
                result = result * ai % M;
                count += c;
            }
            if count == k {
                break;
            }
        }
        if count != k {
            count = 0;
            result = 1;
            for i in 0..a_plus.len() {
                let (ai, c) = a_plus[i];
                if c == 2 {
                    if count + c <= k {
                        result = result * ai % M;
                        count += c;
                    }
                } else {
                    if i < last_plus {
                        result = result * ai % M;
                        count += c;
                    }
                }
                if count == k {
                    break;
                }
            }
            if count != k {
                if a_zero > 0 {
                    a.sort_by_key(|&ai| ai.abs());
                    result = 1;
                    for i in 0..k {
                        result = result * a[i].abs() % M;
                    }
                    result = (M - result) % M;
                } else {
                    result = 0;
                }
            }
        }
    }

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