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:
/*
#[allow(unused_imports)]
use itertools::Itertools;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

type Mint = kyopro_lib::modint::Mint1_000_000_007;

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

    let mut m = vec![];
    let mut p = vec![];
    for a in a {
        if a < 0 {
            m.push(a);
        } else {
            p.push(a);
        }
    }

    m.sort();
    p.sort();

    let mut res = Mint::new(1);
    if k % 2 == 1 && m.len() == n {
        for &a in &m[m.len() - k..] {
            res *= Mint::from_signed(a);
        }
    } else if k == n {
        for &a in m.iter().chain(p.iter()) {
            res *= Mint::from_signed(a);
        }
    } else {
        if k % 2 == 1 {
            res = Mint::from_signed(p.pop().unwrap());
        }

        let mut y = vec![];
        while p.len() >= 2 {
            let a = p.pop().unwrap();
            let b = p.pop().unwrap();
            y.push(a * b);
        }
        y.reverse();
        let mut z = vec![];
        for i in 0..m.len() / 2 {
            z.push(m[i * 2] * m[i * 2 + 1]);
        }
        z.reverse();

        for _ in 0..k / 2 {
            if y.last() < z.last() {
                res *= Mint::from_signed(z.pop().unwrap());
            } else {
                res *= Mint::from_signed(y.pop().unwrap());
            }
        }
    }
    println!("{}", res.val());
}
*/

fn main() {
    let exe = "/tmp/bin120F7A31";
    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>";