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 inv(a: isize, m: isize) -> isize {
    let m = m as i64;
    let mut a = a as i64;
    let mut b = m as i64;
    let mut u = 1;
    let mut v = 0;
    let mut tmp;
    while b != 0 {
        let t = a / b;
        a -= t * b;
        tmp = a;
        a = b;
        b = tmp;
        u -= t * v;
        tmp = u;
        u = v;
        v = tmp;
    }
    u %= m;
    if u < 0 {
        u += m;
    }
    return u as isize;
}

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

    let mut a_plus = vec![];
    let mut a_minus = vec![];
    for i in 0..n {
        let ai = a[i];
        if ai > 0 {
            a_plus.push(ai);
        } else if ai < 0 {
            a_minus.push(ai);
        }
    }

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

    if np + nm < k {
        eprintln!("zero");
        println!("0");
        return;
    }
    if np == 0 && k % 2 == 1 {
        eprintln!("minus");
        a.sort_by_key(|&ai| ai.abs());
        let mut result = 1;
        for i in 0..k {
            result = result * a[i].abs() % M;
        }
        println!("{}", (M - result) % M);
        return;
    }

    a.sort_by_key(|&ai| ai.abs());
    a.reverse();

    let mut result = 1;
    let mut minus_count = 0;
    let mut last_minus = INF;
    let mut last_plus = INF;
    for i in 0..k {
        if a[i] < 0 {
            minus_count += 1;
            last_minus = i;
        } else if a[i] > 0 {
            last_plus = i;
        }
        result = result * a[i].abs() % M;
    }
    if minus_count % 2 == 1 {
        eprintln!("minus");
        let mut next_minus = INF;
        let mut next_plus = INF;
        for i in (k..n).rev() {
            if a[i] < 0 {
                next_minus = i;
            } else if a[i] > 0 {
                next_plus = i;
            }
        }
        let x = if last_minus < INF && next_minus < INF {
            Some(a[last_minus] * a[next_minus])
        } else {
            None
        };
        let y = if last_plus < INF && next_plus < INF {
            Some(a[last_plus] * a[next_plus])
        } else {
            None
        };
        if let Some(x) = x {
            if let Some(y) = y {
                if x > y {
                    result = result * inv(a[last_plus].abs(), M) % M;
                    result = result * a[next_minus].abs() % M;
                } else {
                    result = result * inv(a[last_minus].abs(), M) % M;
                    result = result * a[next_plus].abs() % M;
                }
            } else {
                if last_plus < INF {
                    result = result * inv(a[last_plus].abs(), M) % M;
                }
                result = result * a[next_minus].abs() % M;
            }
        } else {
            if y.is_some() {
                if last_minus < INF {
                    result = result * inv(a[last_minus].abs(), M) % M;
                }
                result = result * a[next_plus].abs() % M;
            } else {
                a.sort_by_key(|&ai| ai.abs());
                result = 1;
                for i in 0..k {
                    result = result * a[i].abs() % M;
                }
                result = (M - result) % M;
            }
        }
    }

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