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: Runtime Error)

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 = 1000000007;
    let k: usize = read();
    let mut a: Vec<i64> = (0..n).map(|_| read()).collect();
    a.sort();
    a.reverse();
    let mut ans: i64 = read();
    let mut l: usize = 0;
    let mut r = n - 1;
    if (k % 2 == 1) {
        ans *= a[0];
        l = 1;
    }
    for i in 0..k / 2 {
        if a[l] * a[l + 1] >= a[r] * a[r - 1] {
            ans = (ans * ((a[l] * a[l + 1]) % MOD));
            l += 2;
        } else {
            ans = ans * ((a[r] * a[r - 1] % MOD) % MOD);
            r -= 2;
        }
    }
    if ans < 0 {
        let mut tmp: i64 = 1;
        for i in 0..k {
            tmp = (tmp * ((a[i]) % MOD)%MOD);
        }
        ans = tmp;
    }
    println!("{}",ans);
}