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 input::Input;

const MOD: i64 = 1000000000 + 7;

fn main() {
    let mut input = Input::default();

    let n = input.parse();
    let k = input.parse();
    let mut a = (0..n).map(|_| input.parse::<i64>()).collect::<Vec<_>>();
    a.sort();

    if k == 1 {
        let mut ans = a[n - 1];
        if ans < 0 {
            ans += MOD;
        }
        println!("{}", ans);
        return;
    }

    if a[n - 1] <= 0 {
        let mut ans = 1;
        for i in 0..k {
            ans *= a[n - 1 - i] % MOD;
            ans %= MOD;
        }
        if ans < 0 {
            ans += MOD;
        }
        println!("{}", ans);
        return;
    }

    let mut l = 0;
    let mut r = n - 1;
    let mut c = 0;
    let mut ans = 1;
    while c < k && l < r {
        let x = a[l] * a[l + 1];
        let y = a[r] * a[r - 1];
        if x > y {
            ans *= x % MOD;
            l += 2;
        } else {
            ans *= y % MOD;
            r -= 2;
        }
        ans %= MOD;
        c += 2;
    }

    if ans < 0 {
        ans += MOD;
    }
    println!("{}", ans);
}

#[allow(dead_code)]
pub mod input {
    #[derive(Default)]
    pub struct Input(Vec<String>);

    impl Input {
        pub fn read_line(&mut self) -> String {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).ok().expect("read error");
            s
        }
        pub fn parse<T: std::str::FromStr>(&mut self) -> T {
            let x = if let Some(x) = self.0.pop() {
                x
            } else {
                let s = self.read_line();
                self.0 = s.split_whitespace().map(String::from).rev().collect();
                self.0.pop().expect("reached EOF")
            };
            x.parse().ok().expect("parse error")
        }
    }
}