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)

#![allow(unused_imports, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}
macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! flush {
    () => {
        std::io::stdout().flush().unwrap();
    };
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;

// @algebra.modint.rs
#[derive(Debug, PartialEq, Eq, Clone, Copy)]
struct ModInt(i64, i64); // (residual, modulo)
impl ModInt {
    fn new(residual: i64, modulo: i64) -> ModInt {
        if residual >= modulo {
            ModInt(residual % modulo, modulo)
        } else if residual < 0 {
            ModInt((residual % modulo) + modulo, modulo)
        } else {
            ModInt(residual, modulo)
        }
    }
    fn unwrap(self) -> i64 {
        self.0
    }
    fn inv(self) -> Self {
        fn exgcd(r0: i64, a0: i64, b0: i64, r: i64, a: i64, b: i64) -> (i64, i64, i64) {
            if r > 0 {
                exgcd(r, a, b, r0 % r, a0 - r0 / r * a, b0 - r0 / r * b)
            } else {
                (a0, b0, r0)
            }
        }
        let (a, _, r) = exgcd(self.0, 1, 0, self.1, 0, 1);
        if r != 1 {
            panic!("{:?} has no inverse!", self);
        }
        ModInt(((a % self.1) + self.1) % self.1, self.1)
    }
    fn pow(self, n: i64) -> Self {
        if n < 0 {
            self.pow(-n).inv()
        } else if n == 0 {
            ModInt(1, self.1)
        } else if n == 1 {
            self
        } else {
            let mut x = (self * self).pow(n / 2);
            if n % 2 == 1 {
                x *= self
            }
            x
        }
    }
}
impl std::fmt::Display for ModInt {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}
impl std::ops::Neg for ModInt {
    type Output = Self;
    fn neg(self) -> Self {
        if self.0 == 0 {
            return self;
        }
        ModInt(self.1 - self.0, self.1)
    }
}
impl std::ops::Add<i64> for ModInt {
    type Output = Self;
    fn add(self, other: i64) -> Self {
        ModInt::new(self.0 + other, self.1)
    }
}
impl std::ops::Add for ModInt {
    type Output = Self;
    fn add(self, other: ModInt) -> Self {
        self + other.0
    }
}
impl std::ops::Add<ModInt> for i64 {
    type Output = ModInt;
    fn add(self, other: ModInt) -> ModInt {
        other + self
    }
}
impl std::ops::AddAssign<i64> for ModInt {
    fn add_assign(&mut self, other: i64) {
        self.0 = ModInt::new(self.0 + other, self.1).0;
    }
}
impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, other: ModInt) {
        *self += other.0;
    }
}
impl std::ops::Sub<i64> for ModInt {
    type Output = Self;
    fn sub(self, other: i64) -> Self {
        ModInt::new(self.0 - other, self.1)
    }
}
impl std::ops::Sub for ModInt {
    type Output = Self;
    fn sub(self, other: ModInt) -> Self {
        self - other.0
    }
}
impl std::ops::Sub<ModInt> for i64 {
    type Output = ModInt;
    fn sub(self, other: ModInt) -> ModInt {
        ModInt::new(self - other.0, other.1)
    }
}
impl std::ops::SubAssign<i64> for ModInt {
    fn sub_assign(&mut self, other: i64) {
        self.0 = ModInt::new(self.0 - other, self.1).0;
    }
}
impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, other: ModInt) {
        *self -= other.0;
    }
}
impl std::ops::Mul<i64> for ModInt {
    type Output = Self;
    fn mul(self, other: i64) -> Self {
        ModInt::new(self.0 * other, self.1)
    }
}
impl std::ops::Mul for ModInt {
    type Output = Self;
    fn mul(self, other: ModInt) -> Self {
        self * other.0
    }
}
impl std::ops::Mul<ModInt> for i64 {
    type Output = ModInt;
    fn mul(self, other: ModInt) -> ModInt {
        other * self
    }
}
impl std::ops::MulAssign<i64> for ModInt {
    fn mul_assign(&mut self, other: i64) {
        self.0 = ModInt::new(self.0 * other, self.1).0;
    }
}
impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, other: ModInt) {
        *self *= other.0;
    }
}
impl std::ops::Div for ModInt {
    type Output = Self;
    fn div(self, other: ModInt) -> Self {
        self * other.inv()
    }
}
impl std::ops::Div<i64> for ModInt {
    type Output = Self;
    fn div(self, other: i64) -> Self {
        self / ModInt(other, self.1)
    }
}
impl std::ops::Div<ModInt> for i64 {
    type Output = ModInt;
    fn div(self, other: ModInt) -> ModInt {
        other.inv() * self
    }
}
impl std::ops::DivAssign for ModInt {
    fn div_assign(&mut self, other: ModInt) {
        self.0 = (self.clone() / other).0;
    }
}
impl std::ops::DivAssign<i64> for ModInt {
    fn div_assign(&mut self, other: i64) {
        *self /= ModInt(other, self.1);
    }
}

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let k: usize = sc.cin();
    let mut xs: Vec<i64> = sc.vec(n);

    if n == k {
        let mut m = ModInt(1, M);
        for &x in xs.iter() {
            m *= x;
        }
        put!(m);
        return;
    }

    if k % 2 == 1 && xs.iter().all(|&x| x < 0) {
        xs.sort();
        xs.reverse();
        let mut m = ModInt(1, M);
        for &x in xs.iter().take(k) {
            m *= x;
        }
        put!(m);
        return;
    }

    xs.sort_by_key(|&x| -x.abs());
    trace!(&xs);

    let mut m = ModInt(1, M);
    let mut sign = 1;
    for &x in xs.iter().take(k) {
        m *= x.abs();
        if x < 0 {
            sign *= -1;
        }
    }
    // trace!(m, sign);
    if sign < 0 {
        let last_neg: Option<&i64> = xs[0..k].iter().rev().filter(|&&x| x < 0).next();
        let last_pos = xs[0..k].iter().rev().filter(|&&x| x >= 0).next();
        let first_neg = xs[k..n].iter().filter(|&&x| x < 0).next();
        let first_pos = xs[k..n].iter().filter(|&&x| x >= 0).next();
        // trace!((last_neg, first_pos), (last_pos, first_neg));
        match ((last_neg, first_pos), (last_pos, first_neg)) {
            ((Some(&ln), Some(&fp)), (Some(&lp), Some(&r#fn))) => {
                if (fp * lp).abs() > (r#fn * ln).abs() {
                    m *= fp.abs();
                    m /= ln.abs();
                } else {
                    m *= r#fn.abs();
                    m /= lp.abs();
                }
            }
            ((Some(&ln), Some(&fp)), _) => {
                m *= fp.abs();
                m /= ln.abs();
            }
            (_, (Some(&lp), Some(&r#fn))) => {
                m *= r#fn.abs();
                m /= lp.abs();
            }
            _ => {}
        }
    }
    put!(m);
}

use std::collections::VecDeque;
use std::io::{self, Write};
use std::str::FromStr;

struct Scanner {
    stdin: io::Stdin,
    buffer: VecDeque<String>,
}
impl Scanner {
    fn new() -> Self {
        Scanner {
            stdin: io::stdin(),
            buffer: VecDeque::new(),
        }
    }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.is_empty() {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> {
        self.cin::<String>().chars().collect()
    }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.cin()).collect()
    }
}