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)

use std::io;
use std::str::FromStr;
use std::cmp::max;

static MOD: i64 = 1_000_000_007;

fn input_tuple() -> (i64, i64) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<i64> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1])
}

fn input_vec() -> Vec<i64> {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    line.split_whitespace().map(|s| s.parse().unwrap()).collect()
}


fn main() {
    let (n, k) = input_tuple();
    let a_vec = input_vec();

    if n == k {
        let mut ans = 1;
        for a in a_vec {
            ans = ans * a % MOD;
        }
        println!("{}", (MOD + ans) % MOD);
        return;
    }
    let mut a_sei: Vec<i64> = Vec::new();
    let mut a_fu: Vec<i64> = Vec::new();
    for a in a_vec {
        if a >= 0 {
            a_sei.push(a);
        } else {
            a_fu.push(a);
        }
    }
    a_sei.sort_by(|x, y| y.cmp(&x));
    a_fu.sort();
    
    if a_sei.len() == 0 && k % 2 == 1 {
        let mut ans = 1;
        for i in 0..k as usize {
            ans = ans * a_fu[a_fu.len() - 1 - i] % MOD;
        }
        println!("{}", (ans + MOD) % MOD);
        return;
    }
    let mut i = 0usize;
    while i <= k as usize {
        // println!("i = {}", i);
        if i + 1 >= a_fu.len() || k as usize - i < 2 {
            break;                
        } else if k - i as i64 - 1 >= a_sei.len() as i64 {
            i += 2;
            continue;
        } else if a_fu[i] * a_fu[i+1] > a_sei[k as usize - i - 1] * a_sei[k as usize - i - 2] {
            i += 2;
        } else {
            break;
        }
    }
    let mut ans = 1;
    // println!("{}: {}, {}", i, a_sei.len(), a_fu.len());
    for j in 0..i {
        ans *= a_fu[j as usize];
        ans %= MOD;
    }
    for j in 0..k - i as i64 {
        ans *= a_sei[j as usize];
        ans %= MOD;
    }
    println!("{}", ans);
    return;
}