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)]
use itertools::Itertools;
use num_traits::clamp;
use ordered_float::OrderedFloat;
use proconio::{fastout, input, marker::*};
use std::cmp::*;
use std::collections::*;
use superslice::*;

#[fastout()]
fn main() {
    input! {
        n: usize, k: usize,
        mut a: [i64; n],
    }
    let m = 1000000007i64;
    let mod_product = |acc: i64, &value: &i64| {
        (acc * value).rem_euclid(m)
    };

    if k == n || k % 2 == 1 && a.iter().all(|v| *v <= 0) {
        a.sort_by_key(|v| -*v);
        let ans = a.iter().take(k).fold(1, mod_product);
        println!("{}", ans);
        return;
    }

    a.sort_by_key(|v| Reverse(v.abs()));
    let mut plus = Vec::new();
    let mut minus = Vec::new();
    for i in 0..n {
        if a[i] >= 0 {
            plus.push(a[i]);
        } else {
            minus.push(a[i]);
        }
    }

    let mut ppos = 0;
    let mut mpos = 0;
    let mut vals = Vec::new();
    let mut retry = false;
    while vals.len() < k {
        if vals.len() < k - 1 && ppos + 1< plus.len() && mpos + 1 < minus.len() {
            if plus[ppos] * plus[ppos+1] < minus[mpos] * minus[mpos+1] {
                vals.push(minus[mpos]);
                vals.push(minus[mpos+1]);
                mpos += 2;
            } else {
                vals.push(plus[ppos]);
                vals.push(plus[ppos+1]);
                ppos += 2;
            }
        } else if vals.len() < k - 1 && mpos + 1 < minus.len() {
            vals.push(minus[mpos]);
            vals.push(minus[mpos+1]);
            mpos += 2;
        } else if ppos < plus.len() {
            vals.push(plus[ppos]);
            ppos += 1;
        } else {
            retry = true;
            break;
        }
    }
    let ans = if !retry {
        vals.iter().fold(1, mod_product)
    } else {
        a.sort_by_key(|v| v.abs());
        assert!(k % 2 == 1);
        assert!(a.iter().filter(|v| **v < 0).count() > 2);
        a.iter().take(k).fold(1, mod_product)
    };
    println!("{}", ans);
}