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: Wrong Answer)

use std::cmp::*;
use std::collections::*;
use std::io::*;
use std::str::FromStr;
fn read<T: FromStr>() -> 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().expect("failed to parse token")
}
fn main() {
    let n: usize = read();
    let MOD = (1e9 + 7 as f64) as i64;
    let k: usize = read();
    let mut a: Vec<i64> = (0..n).map(|_| read()).collect();
    let mut pos: Vec<i64> = Vec::new();
    let mut neg: Vec<i64> = Vec::new();
    for i in &a {
        if i < &0 {
            neg.push(*i);
        } else {
            pos.push(*i);
        }
    }
    let mut pos_size = pos.len();
    let mut neg_size = neg.len();
    let mut ok: bool = false;
    if pos_size > 0 {
        if n == k {
            ok = (neg_size % 2 == 0);
        } else {
            ok = true;
        }
    } else {
        ok = (k % 2 == 0);
    }
    let mut ans: i64 = 1;
    if !ok {
        a.sort_by_key(|x| x.abs());
        for i in 0..k {
            ans = ans * a[i] % MOD;
            ans %= MOD;
        }
    } else {
        pos.sort();
        neg.sort();
        neg.reverse();
        if k % 2 == 1 {
            ans = ans * pos[pos.len() - 1] % MOD;
            ans %= MOD;
            pos.pop();
        }
        let mut p: Vec<i64> = Vec::new();
        while (pos.len() >= 2) {
            let mut x = pos[pos.len() - 1];
            pos.pop();
            x *= pos[pos.len() - 1] % MOD;
            x %= MOD;
            pos.pop();
            p.push(x);
        }
        while (neg.len() >= 2) {
            let mut x = neg[neg.len() - 1];
            neg.pop();
            x *= neg[neg.len() - 1] % MOD;
            x %= MOD;
            neg.pop();
            p.push(x);
        }
        p.sort();
        p.reverse();
        for i in 0..k / 2 {
            ans = ans * p[i] % MOD;
            ans %= MOD;
        }
    }
    println!("{}", (ans + MOD) % MOD);
}