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)

#[macro_use]
mod input_mcr {
    // ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
    // diff: using Parser
    #[macro_export(local_inner_macros)]
    macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut parser = Parser::from_str($s);
        input_inner!{parser, $($r)*}
    };
    (parser = $parser:ident, $($r:tt)*) => {
        input_inner!{$parser, $($r)*}
    };
    (new_stdin_parser = $parser:ident, $($r:tt)*) => {
        let stdin = std::io::stdin();
        let reader = std::io::BufReader::new(stdin.lock());
        let mut $parser = Parser::new(reader);
        input_inner!{$parser, $($r)*}
    };
    ($($r:tt)*) => {
        input!{new_stdin_parser = parser, $($r)*}
    };
}

    #[macro_export(local_inner_macros)]
    macro_rules! input_inner {
    ($parser:ident) => {};
    ($parser:ident, ) => {};
    ($parser:ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($parser, $t);
        input_inner!{$parser $($r)*}
    };
}

    #[macro_export(local_inner_macros)]
    macro_rules! read_value {
    ($parser:ident, ( $($t:tt),* )) => {
        ( $(read_value!($parser, $t)),* )
    };
    ($parser:ident, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
    };
    ($parser:ident, chars) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()
    };
    ($parser:ident, char_) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()[0]
    };
    ($parser:ident, usize1) => {
        read_value!($parser, usize) - 1
    };
    ($parser:ident, line) => {
        $parser.next_line()
    };
    ($parser:ident, line_) => {
        $parser.next_line().chars().collect::<Vec<char>>()
    };
    ($parser:ident, i64_) => {
        $parser.fast_i64()
    };
    ($parser:ident, usize_) => {
        $parser.fast_i64() as usize
    };
    ($parser:ident, usize1_) => {
        ($parser.fast_i64() - 1) as usize
    };
    ($parser:ident, $t:ty) => {
        $parser.next::<$t>().expect("Parse error")
    };
}

    use std::io;
    use std::io::BufRead;
    use std::str;

    // ref: tatsuya6502 <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e>
    // ref: wariuni <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e#comment-7040a5ae96305e884eb9>
    // diff: using std::io::BufRead::fill_buf()
    pub struct Parser<R> {
        pub reader: R,
        buf: Vec<u8>,
        pos: usize,
    }

    impl Parser<io::Empty> {
        pub fn from_str(s: &str) -> Parser<io::Empty> {
            Parser {
                reader: io::empty(),
                buf: s.as_bytes().to_vec(),
                pos: 0,
            }
        }
    }

    impl<R: BufRead> Parser<R> {
        pub fn new(reader: R) -> Parser<R> {
            Parser {
                reader: reader,
                buf: vec![],
                pos: 0,
            }
        }
        pub fn update_buf(&mut self) {
            self.buf.clear();
            self.pos = 0;
            loop {
                let (len, complete) = {
                    let buf2 = self.reader.fill_buf().unwrap();
                    self.buf.extend_from_slice(buf2);
                    let len = buf2.len();
                    (len, buf2[len - 1] <= 0x20)
                };
                self.reader.consume(len);
                if complete {
                    break;
                }
            }
        }
        pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
            loop {
                let mut begin = self.pos;
                while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                    begin += 1;
                }
                let mut end = begin;
                while end < self.buf.len() && (self.buf[end] > 0x20) {
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.parse::<T>();
                } else {
                    self.update_buf();
                }
            }
        }
        pub fn next_line(&mut self) -> String {
            loop {
                let mut begin = self.pos;
                if begin < self.buf.len() && (self.buf[begin] < 0x20) {
                    begin += 1;
                }
                let mut end = begin;
                while end < self.buf.len() && (self.buf[end] >= 0x20) {
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.to_string();
                } else {
                    self.update_buf();
                }
            }
        }
        pub fn fast_i64(&mut self) -> i64 {
            loop {
                let mut begin = self.pos;
                while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                    begin += 1;
                }
                if begin == self.buf.len() {
                    self.update_buf();
                    continue;
                }
                let mut res = 0;
                let (is_positive, mut end) = match self.buf[begin] {
                    b'+' => (true, begin + 1),
                    b'-' => (false, begin + 1),
                    _ => (true, begin),
                };
                while end < self.buf.len() && (self.buf[end] > 0x20) {
                    res = res * 10 + (self.buf[end] as i64 - '0' as i64);
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return if is_positive { res } else { -res };
                } else {
                    self.update_buf();
                }
            }
        }
    }
}

use crate::input_mcr::*;
use std::cmp::*;

use std::collections::VecDeque;

fn main() {
    input! {
        n: usize,
        m: usize,
        xs: [i64; n],
    }
    let mut xs = xs;
    let mut ys = VecDeque::new();
    let mut zs = VecDeque::new();
    xs.sort();
    for &x in &xs {
        if x < 0 {
            zs.push_back(x);
        } else {
            ys.push_front(x);
        }
    }
    let mut fail = false;
    xs.sort();
    const Mod: i64 = 1_000_000_007i64;
    {
        let mut res = 1;
        let mut rem = m;
        let mut ys = VecDeque::new();
        let mut zs = VecDeque::new();
        for &x in &xs {
            if x < 0 {
                zs.push_back(x);
            } else {
                ys.push_front(x);
            }
        }
        while rem != 0 {
            if rem >= 2 {
                if ys.len() >= 2 {
                    if zs.len() >= 2 {
                        if ys[0] * ys[1] > zs[0] * zs[1] {
                            res = (res * ys[0]) % Mod;
                            res = (res * ys[1]) % Mod;
                            ys.pop_front();
                            ys.pop_front();
                            rem -= 2;
                            continue;
                        } else {
                            res = (res * zs[0]) % Mod;
                            res = (res * zs[1]) % Mod;
                            zs.pop_front();
                            zs.pop_front();
                            rem -= 2;
                            continue;
                        }
                    } else {
                        res = (res * ys[0]) % Mod;
                        res = (res * ys[1]) % Mod;
                        ys.pop_front();
                        ys.pop_front();
                        rem -= 2;
                        continue;
                    }
                } else {
                    if zs.len() >= 2 {
                        res = (res * zs[0]) % Mod;
                        res = (res * zs[1]) % Mod;
                        zs.pop_front();
                        zs.pop_front();
                        rem -= 2;
                        continue;
                    } else {
                        // eprintln!("fail!");
                        fail = true;
                        break;
                    }
                }
            } else if rem == 1 {
                if ys.len() >= 1 {
                    res = (res * ys[0]) % Mod;
                    rem -= 1;
                    continue;
                } else {
                    // eprintln!("fail!!!");
                    fail = true;
                    break;
                }
            } else {
                // eprintln!("fail!!");
                fail = true;
                break;
            }
        }
        if !fail {
            println!("{}", res);
            return;
        }
    }
    {
        let mut res = 1;
        let mut rem = m;
        let mut ys = VecDeque::new();
        let mut zs = VecDeque::new();
        for &x in &xs {
            if x < 0 {
                zs.push_front(x);
            } else {
                ys.push_back(x);
            }
        }
        while rem != 0 {
            if rem >= 2 {
                if ys.len() >= 2 {
                    if zs.len() >= 2 {
                        if ys[0] * ys[1] < zs[0] * zs[1] {
                            res = (res * ys[0]) % Mod;
                            res = (res * ys[1]) % Mod;
                            ys.pop_front();
                            ys.pop_front();
                            rem -= 2;
                            continue;
                        } else {
                            res = (res * zs[0]) % Mod;
                            res = (res * zs[1]) % Mod;
                            zs.pop_front();
                            zs.pop_front();
                            rem -= 2;
                            continue;
                        }
                    } else {
                        res = (res * ys[0]) % Mod;
                        res = (res * ys[1]) % Mod;
                        ys.pop_front();
                        ys.pop_front();
                        rem -= 2;
                        continue;
                    }
                } else {
                    if zs.len() >= 2 {
                        res = (res * zs[0]) % Mod;
                        res = (res * zs[1]) % Mod;
                        zs.pop_front();
                        zs.pop_front();
                        rem -= 2;
                        continue;
                    } else {
                        // eprintln!("fail! (2)");
                        return;
                    }
                }
            } else if rem == 1 {
                if ys.len() >= 1 {
                    // eprintln!("fail (4)");
                } else {
                    res = ((res * zs[0]) % Mod + Mod) % Mod;
                    // eprintln!("ok?");
                    break;
                }
            } else {
                // eprintln!("fail!!");
                fail = true;
                break;
            }
        }
        println!("{}", res);
        return;
    }
}