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 proconio::{input,fastout};

const MOD: u64 = 1000000007;

#[fastout]
fn main() {
    input! {
        n: usize,
        k: usize,
    }

    let mut vp: Vec<u64> = Vec::with_capacity(200010);
    let mut vm: Vec<u64> = Vec::with_capacity(200010);
    let mut ps = 0;
    let mut zs = 0;
    let mut ms = 0;

    for _ in 0..n {
        input! {
            mut a: i64,
        }
        if a > 0 {
            vp.push(a as u64);
            ps += 1;
        }
        else if a < 0 {
            a = -a;
            vm.push(a as u64);
            ms += 1;
        }
        else {
            zs += 1;
        }
    }

    let mut ans: u64 = 1;

    if zs + k > n {
        ans = 0;
    }
    else if k == n {
        if zs > 0 {
            ans = 0;
        }
        else {
            for i in &vp {
                ans = (ans * i) % MOD;
            }
            for i in &vm {
                ans = (ans * i) % MOD;
            }
            if ms % 2 == 1 {
                ans = (2 * MOD - ans) % MOD;
            }
        }
    }
    else if k % 2 == 1 && ms == n {
        vm.sort_unstable();
        for i in 0..k {
            ans = (ans * vm[i]) % MOD;
        }
        ans = (2 * MOD - ans) % MOD;
    }
    else {
        vp.sort_unstable();
        vp.reverse();
        vm.sort_unstable();
        vm.reverse();
        let mut i: usize = 0;
        let mut j: usize = 0;
        loop {
            if i + j >= k {
                break;
            }
            else if i >= ps {
                ans = (ans * vm[j]) % MOD;
                j += 1;
            }
            else if j >= ms {
                ans = (ans * vp[i]) % MOD;
                i += 1;
            }
            else if vp[i] >= vm[j] {
                ans = (ans * vp[i]) % MOD;
                i += 1;
            }
            else {
                ans = (ans * vm[j]) % MOD;
                j += 1;
            }
        }
        if j % 2 == 1 {
            if i == ps && j == ms {
                ans = 0;
            }
            else if i == 0 {
                if ps == 0 {
                    ans = 0;
                }
                else {
                    ans = 1;
                    if j >= 2 {
                        for j1 in 0..(j-1) {
                            ans = (ans * vm[j1]) % MOD;
                        }
                    }
                    ans = (ans * vp[0]) % MOD;
                }
            }
            else if i == ps {
                ans = 1;
                if i >= 2 {
                    for i1 in 0..(i-1) {
                        ans = (ans * vp[i1]) % MOD;
                    }
                }
                for j1 in 0..=j {
                    ans = (ans * vm[j1]) % MOD;
                }
            }
            else if j == ms {
                ans = 1;
                for i1 in 0..=i {
                    ans = (ans * vp[i1]) % MOD;
                }
                if j >= 2 {
                    for j1 in 0..(j-1) {
                        ans = (ans * vm[j1]) % MOD;
                    }
                }
            }
            else {
                if vp[i-1] * vp[i] >= vm[j-1] * vm[j] {
                    ans = 1;
                    for i1 in 0..=i {
                        ans = (ans * vp[i1]) % MOD;
                    }
                    if j >= 2 {
                        for j1 in 0..(j-1) {
                            ans = (ans * vm[j1]) % MOD;
                        }
                    }
                }
                else {
                    ans = 1;
                    if i >= 2 {
                        for i1 in 0..(i-1) {
                            ans = (ans * vp[i1]) % MOD;
                        }
                    }
                    for j1 in 0..=j {
                        ans = (ans * vm[j1]) % MOD;
                    }
                }
            }
        }
    }
    println!("{}",ans);
}