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,
    unused_variables,
    unused_assignments,
    unused_mut,
    unused_imports,
    dead_code
)]
//use proconio::fastout;
use proconio::input;
use proconio::marker::*;
use std::cmp::*;
use std::collections::*;
//use std::collections::VecDeque;

const MOD: i64 = 1_000_000_007;
fn main() {
    input! {
       N:usize,mut K:usize,
       mut A:[i64;N]
    }
    let mut poslist = Vec::with_capacity(N);
    let mut neglist = Vec::with_capacity(N);
    let mut zerolen = 0;
    for i in 0..N {
        if A[i] == 0 {
            zerolen += 1;
        } else if A[i] > 0 {
            poslist.push(A[i]);
        } else {
            neglist.push(A[i]);
        }
    }
    let mut ans = 1;
    if N - zerolen < K {
        println!("0");
        return;
    }
    if N - zerolen == K && zerolen > 0 && neglist.len() % 2 != 0 {
        println!("0");
        return;
    }
    if poslist.len() == 0 {
        // この時 neglist.len() >= K
        neglist.sort();
        if K % 2 == 1 {
            if zerolen > 0 {
                println!("0");
                return;
            }
            neglist.reverse();
        }
        for i in 0..K {
            ans = ans * neglist[i] % MOD;
        }
    } else if N == K {
        for l in 0..N {
            ans = ans * A[l] % MOD;
        }
    } else {
        // poslist.len()>0のケース。
        neglist.sort();
        poslist.sort();
        poslist.reverse();
        let mut i = 0;
        let mut j = 0;
        if K % 2 == 1 {
            i = 1;
            K -= 1;
        }
        for k in 0..(K / 2) {
            if i + 1 >= poslist.len() {
                j += 2;
            } else if j + 1 >= neglist.len() {
                i += 2;
            } else if poslist[i] * poslist[i + 1] >= neglist[j] * neglist[j + 1] {
                i += 2;
            } else {
                j += 2;
            }
        }
        for l in 0..i {
            ans = ans * poslist[l] % MOD;
        }
        for l in 0..j {
            ans = ans * neglist[l] % MOD;
        }
    }
    println!("{}", (ans + MOD) % MOD);
}