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

use std::str::FromStr;
use std::io::*;
use std::collections::*;
use std::cmp::*;

struct Scanner<I: Iterator<Item = char>> {
    iter: std::iter::Peekable<I>,
}

macro_rules! exit {
    () => {{
        exit!(0)
    }};
    ($code:expr) => {{
        if cfg!(local) {
            writeln!(std::io::stderr(), "===== Terminated =====")
                .expect("failed printing to stderr");
        }
        std::process::exit($code);
    }}
}

impl<I: Iterator<Item = char>> Scanner<I> {
    pub fn new(iter: I) -> Scanner<I> {
        Scanner {
            iter: iter.peekable(),
        }
    }

    pub fn safe_get_token(&mut self) -> Option<String> {
        let token = self.iter
            .by_ref()
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        if token.is_empty() {
            None
        } else {
            Some(token)
        }
    }

    pub fn token(&mut self) -> String {
        self.safe_get_token().unwrap_or_else(|| exit!())
    }

    pub fn get<T: FromStr>(&mut self) -> T {
        self.token().parse::<T>().unwrap_or_else(|_| exit!())
    }

    pub fn vec<T: FromStr>(&mut self, len: usize) -> Vec<T> {
        (0..len).map(|_| self.get()).collect()
    }

    pub fn mat<T: FromStr>(&mut self, row: usize, col: usize) -> Vec<Vec<T>> {
        (0..row).map(|_| self.vec(col)).collect()
    }

    pub fn char(&mut self) -> char {
        self.iter.next().unwrap_or_else(|| exit!())
    }

    pub fn chars(&mut self) -> Vec<char> {
        self.get::<String>().chars().collect()
    }

    pub fn mat_chars(&mut self, row: usize) -> Vec<Vec<char>> {
        (0..row).map(|_| self.chars()).collect()
    }

    pub fn line(&mut self) -> String {
        if self.peek().is_some() {
            self.iter
                .by_ref()
                .take_while(|&c| !(c == '\n' || c == '\r'))
                .collect::<String>()
        } else {
            exit!();
        }
    }

    pub fn peek(&mut self) -> Option<&char> {
        self.iter.peek()
    }
}

use std::ops::*;
use std::fmt;

#[derive(Copy, Clone, PartialEq, Debug)]
struct ModInt(usize);

const MOD: usize = 1000000007;
impl ModInt {
    fn new(n: i64) -> Self {
        ModInt((n % MOD as i64 + MOD as i64) as usize % MOD)
    }

    fn pow(self, power: usize) -> Self {
        if power == 0 {
            return ModInt(1);
        }
        if power % 2 == 0 {
            let t = self.pow(power/2);
            return t * t;
        }
        self * self.pow(power-1)
    }

    fn inv(self) -> Self {
        self.pow(MOD - 2)
    }
}

impl Add for ModInt {
    type Output = Self;

    fn add(self, rhs: Self) -> Self {
        let mut tmp = self;
        tmp.0 += rhs.0;
        if tmp.0 >= MOD {
            tmp.0 -= MOD;
        }
        tmp
    }
}

impl AddAssign for ModInt {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl Sub for ModInt {
    type Output = Self;

    fn sub(self, rhs: Self) -> Self {
        let mut ret = self;
        if ret.0 < rhs.0 {
            ret.0 += MOD;
        }
        ret.0 -= rhs.0;
        ret
    }
}

impl SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

impl Mul for ModInt {
    type Output = Self;

    fn mul(self, rhs: ModInt) -> Self {
        let mut ret = self;
        ret.0 *= rhs.0;
        ret.0 %= MOD;
        ret
    }
}

impl MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl Div for ModInt {
    type Output = ModInt;

    fn div(self, rhs: ModInt) -> Self {
        let mut ret = self;
        ret.0 *= rhs.inv().0;
        ret.0 %= MOD;
        ret
    }
}

impl DivAssign for ModInt {
    fn div_assign(&mut self, rhs: Self) {
        *self = *self / rhs;
    }
}

impl fmt::Display for ModInt {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(f, "{}", self.0)
    }
}

fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin.bytes().map(|c| c.unwrap() as char));
    let N: usize = sc.get();
    let K: usize = sc.get();
    let mut A: Vec<i64> = sc.vec(N);
    let mut pos = Vec::new();
    let mut neg = Vec::new();
    for i in 0..N {
        if A[i] >= 0 {
            pos.push(A[i]);
        } else {
            neg.push(A[i]);
        }
    }
    let mut can_pos = false;
    if pos.len() > 0 {
        if N == K {
            if neg.len() % 2 == 0 {
                can_pos = true;
            }
        } else {
            can_pos = true;
        }
    } else {
        if K % 2 == 0 {
            can_pos = true;
        }
    }
    let mut ans = ModInt(1);
    if !can_pos {
        A.sort_by_key(|&i| i.abs());
        for i in 0..K {
            ans *= ModInt::new(A[i]);
        }
        println!("{}", ans);
    } else {
        pos.sort_by_key(|&i| Reverse(i.abs()));
        neg.sort_by_key(|&i| Reverse(i.abs()));
        let mut cnt = 0;
        let mut i = 0;
        let mut j = 0;
        if K % 2 != 0 {
            ans *= ModInt::new(pos[i]);
            i += 1;
            cnt += 1;
        }
        while cnt < K {
            if neg.len() - j == 0 || neg.len() - j == 1 {
                ans *= ModInt::new(pos[i]) * ModInt::new(pos[i+1]);
                i += 2;
            } else if pos.len() - i == 0 || pos.len() - i == 1 {
                ans *= ModInt::new(neg[j]) * ModInt::new(neg[j+1]);
                j += 2;
            } else if pos[i] * pos[i+1] < neg[j] * neg[j+1] {
                ans *= ModInt::new(neg[j]) * ModInt::new(neg[j+1]);
                j += 2;
            } else {
                ans *= ModInt::new(pos[i]) * ModInt::new(pos[i+1]);
                i += 2;
            }
            cnt += 2;
        }
        println!("{}", ans);
    }
}