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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
const MOD: u64 = 1000000007;

fn pro(aa: &Vec<u64>, l: usize, r: usize) -> u64 {
    let mut ans = 1;
    let (l, r) = if l < r { (l, r) } else { (r, l) };
    let mut tmp = l;
    while tmp < r {
        ans *= aa[tmp];
        ans %= MOD;
        tmp += 1;
    }

    ans
}

fn main() {
    use proconio::input;
    input!(n: usize, k: usize);
    input!(aa: [i64; n]);

    let mut non_neg = Vec::new();
    let mut neg = Vec::new();

    for &a in aa.iter() {
        if a >= 0 {
            non_neg.push(a as u64);
        } else {
            neg.push((-a) as u64);
        }
    }

    non_neg.sort();
    non_neg.reverse(); // 3, 2, 1
    neg.sort();
    neg.reverse(); // 3, 2, 1 == -3, -2, -1

    if n == k {
        let mut ans = pro(&non_neg, 0, non_neg.len());
        ans *= pro(&neg, 0, neg.len());
        ans %= MOD;
        if neg.len() % 2 == 1 {
            ans = MOD - ans;
        }
        println!("{}", ans);
        return;
    } else if non_neg.len() == 0 && k % 2 == 1 {
        // マイナスになるので後ろから
        let mut ans = pro(&neg, n - k, n);
        ans = MOD - ans;
        println!("{}", ans);
        return;
    }

    let mut k = k;
    let mut ans: u64 = 1;
    if k % 2 == 1 {
        ans *= non_neg.pop().unwrap();
        k -= 1;
    }
    // k % 2 == 0
    while k > 0 {
        let np = if non_neg.len() < 2 {
            0
        } else {
            non_neg[0] * non_neg[1] % MOD
        };
        let n = if neg.len() < 2 {
            0
        } else {
            neg[0] * neg[1] % MOD
        };
        if np > n {
            ans *= np;
            non_neg.pop();
            non_neg.pop();
        } else {
            ans *= n;
            neg.pop();
            neg.pop();
        }
        ans %= MOD;

        k -= 2;
    }

    println!("{}", ans);
}
*/

fn main() {
    let exe = "/tmp/bin2ACF7B16";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";