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)]
use std::io::{stdin, Read};
use std::str::FromStr;
fn read_option<T: FromStr>() -> Option<T> {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok()
}
fn read<T: FromStr>() -> T {
    let opt = read_option();
    opt.expect("failed to parse token")
}

fn main() {
    let N: usize = read();
    let K: usize = read();
    let mut vec: Vec<i64> = (0..N).map(|_| read()).collect();
    let MOD = 10_i64.pow(9) + 7;
    vec.sort();
    if vec.iter().all(|&x| x < 0) && K % 2 == 1 {
        vec.reverse();
        let mut tmp: i64 = 1;
        for &i in &vec[0..K] {
            tmp *= i as i64;
            tmp %= MOD;
        }
        println!("{}", tmp + MOD);
        return;
    }
    let mut negatives: Vec<i64> = vec
        .iter()
        .filter(|&x| x < &0)
        .copied()
        .map(|x| -x)
        .collect();
    let mut positives: Vec<i64> = vec.iter().filter(|&x| x >= &0).copied().collect();
    negatives.sort();
    positives.sort();
    let mut ans_vec: Vec<i64> = vec![];
    while ans_vec.len() != K {
        if positives.is_empty() {
            let v = negatives.pop().unwrap();
            ans_vec.push(-v);
            continue;
        }
        if negatives.len() < 2 {
            let v = positives.pop().unwrap();
            ans_vec.push(v);
            continue;
        }
        if K - ans_vec.len() == 1 {
            let v = positives.pop().unwrap();
            ans_vec.push(v);
            continue;
        }
        if positives.len() == 1 && K - ans_vec.len() >= 2 {
            let v1 = negatives.pop().unwrap();
            let v2 = negatives.pop().unwrap();
            ans_vec.push(-v1);
            ans_vec.push(-v2);
            continue;
        }
        let neg = negatives[negatives.len() - 1] * negatives[negatives.len() - 2];
        let pos = positives[positives.len() - 1] * positives[positives.len() - 2];
        if pos > neg {
            let v = positives.pop().unwrap();
            ans_vec.push(v);
        } else {
            let v1 = negatives.pop().unwrap();
            let v2 = negatives.pop().unwrap();
            ans_vec.push(-v1);
            ans_vec.push(-v2);
        }
    }
    let mut ans: i64 = 1;
    for v in ans_vec {
        ans *= v;
        ans %= MOD;
    }
    if ans < 0 {
        ans += MOD;
    }
    println!("{}", ans)
}