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: Accepted)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use itertools::Itertools;
use proconio::input;
use ralgo::util::modint::{self, One};

struct Modular();
impl modint::Modular for Modular {
    type I = i32;
    type II = i64;

    fn modular() -> Self::I {
        1000000007
    }

    fn convert(ii: Self::II) -> Self::I {
        ii as Self::I
    }
}
type ModInt = modint::ModInt<Modular>;

fn main() {
    input! {
        n: usize,
        k: usize,
        mut a: [i64; n],
    };
    if n == k {
        let res: ModInt = a.iter().cloned().map(ModInt::from_large).product();
        println!("{}", res);
        return;
    }
    let mut negatives = a
        .iter()
        .cloned()
        .filter(|x| *x < 0)
        .map(|x| -x)
        .collect_vec();
    let mut positives = a.iter().cloned().filter(|x| *x > 0).collect_vec();
    if negatives.len() + positives.len() < k {
        println!("0");
        return;
    }
    negatives.sort();
    positives.sort();
    let has_zero = positives.len() + negatives.len() != n;
    if positives.is_empty() {
        if k % 2 == 0 {
            let res: ModInt = negatives
                .iter()
                .rev()
                .take(k)
                .cloned()
                .map(ModInt::from_large)
                .product();
            println!("{}", res)
        } else if has_zero {
            println!("0")
        } else {
            let res: ModInt = negatives
                .iter()
                .take(k)
                .cloned()
                .map(ModInt::from_large)
                .product();
            println!("{}", -res)
        }
    } else {
        let mut res = ModInt::one();
        if k % 2 == 1 {
            res = ModInt::from_large(positives.pop().unwrap())
        }
        let mut pairs = positives
            .iter()
            .rev()
            .tuple_windows()
            .map(|(a, b)| a * b)
            .step_by(2)
            .collect_vec();
        pairs.extend(
            negatives
                .iter()
                .rev()
                .tuple_windows()
                .map(|(a, b)| a * b)
                .step_by(2),
        );
        pairs.sort();
        res *= pairs
            .iter()
            .rev()
            .take(k / 2)
            .cloned()
            .map(ModInt::from_large)
            .product();
        println!("{}", res)
    }
}
*/

fn main() {
    let exe = "/tmp/binF7C0A12C";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";