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)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

#[fastout]
fn main() {
    input! {
         n:usize,k:usize,
    mut      a:[i64;n],
     }
    let mut native_a = a.clone();
    native_a.sort();
    native_a.reverse();
    a.sort_by_key(|&x| -x.abs() as i64);
    dbg!(&a);

    let mut neg = Vec::new();
    let mut pos = Vec::new();
    let mut zero = 0;
    for &x in a.iter() {
        if x <= 0 {
            neg.push(x);
        } else if x > 0 {
            pos.push(x);
        }
        if x == 0 {
            zero += 1;
        }
    }
    let nl = neg.len();
    let pl = pos.len();
    let mut ans = 1i64;
    if k == n {
        for i in 0..n {
            ans = (ans * a[i] + MOD) % MOD;
        }
        ans = (ans + 111 * MOD) % MOD;
        println!("{}", ans);
        return;
    }

    let K = k;
    let mut k = k;
    let mut pn = 0;
    let mut pp = 0;
    while k > 0 {
        if k == 1 {
            if pp < pl {
                ans *= pos[pp];
                ans %= MOD;
                k -= 1;
                break;
            } else {
                // neg
                // println!("KJLJLJ");
                let mut ret = 1i64;
                for i in 0..K {
                    ret *= a[n - i - 1];
                    // dbg!(a[n - i - 1]);
                    ret = (ret + MOD) % MOD;
                }
                ans = ret;
                break;
            }
        } else {
            if (if pp + 1 < pl {
                pos[pp] * pos[pp + 1]
            } else {
                0
            }) > (if pn + 1 < nl {
                neg[pn] * neg[pn + 1]
            } else {
                0
            }) {
                ans *= pos[pp];
                k -= 1;
            } else {
                ans *= neg[pn] * neg[pn + 1];
                k -= 2;
            }
            ans = (ans + 2 * MOD) % MOD;
        }
    }
    println!("{}", (ans + MOD) % MOD);

    // // pにできるか
    // // 正の値にできそう
    // if pl + nl / 2 * 2 >= k {
    //     if k % 2 == 1 && pl == 0 {
    //         println!("{}", 0);
    //     } else {
    //         // がん
    //         let mut np = 0;
    //         let mut pp = 0;
    //         let mut k = k;
    //     }
    // } else {
    //     println!("{}", 0);
    // }

    // // // 負になる
    // if k > pl && (k - pl) % 2 == 1 {
    //     if zero > 0 {
    //         println!("{}", 0);
    //         return;
    //     } else {
    //         let mut ans = 1i64;
    //         for i in 0..k {
    //             ans *= a[n - i - 1];
    //             ans = (ans + 5 * MOD) % MOD;
    //         }
    //         println!("{}", ans);
    //         return;
    //     }
    // } else if pl == 0 {
    //     let mut ans = 1i64;
    //     for i in 0..k {
    //         ans *= (neg[nl - i - 1]);
    //         ans = (ans + 2 * MOD) % MOD;
    //     }
    //     println!("{}", ans);
    //     return;
    // } else if nl == 0 {
    //     let mut ans = 1i64;
    //     for i in 0..k {
    //         ans *= pos[i];
    //         ans = ans % MOD;
    //     }
    //     println!("{}", ans);
    //     return;
    // } else if n == k {
    //     let mut ans = 1i64;
    //     for i in 0..n {
    //         ans = (ans * a[i] + 12 * MOD) % MOD;
    //     }
    //     println!("{}", ans);
    // } else {
    //     let mut indn = 0;
    //     let mut indp = 0;
    //     let mut ans = 1i64;
    //     let mut k = k;
    //     if k == 1 {
    //         println!("{}", pos[0]);
    //         return;
    //     }

    //     while k >= 2 {
    //         if if indn + 1 < nl {
    //             neg[indn] * neg[indn + 1]
    //         } else {
    //             -INF
    //         } >= if indp + 1 < pl {
    //             pos[indp] * pos[indp + 1]
    //         } else {
    //             -INF
    //         } {
    //             ans *= neg[indn] * neg[indn + 1];
    //             indn += 2;
    //         } else {
    //             ans *= pos[indp] * pos[indp + 1];
    //             indp += 2;
    //         }
    //         ans = (ans + 33 * MOD) % MOD;
    //         k -= 2;
    //     }
    //     if k == 0 {
    //         println!("{}", (ans + 33 * MOD) % MOD);
    //         return;
    //     } else {
    //         if indp < pl {
    //             println!("{}", (ans * pos[indp] % MOD + 55 * MOD) % MOD);
    //             return;
    //         } else {
    //             ans = 1i64;
    //             for i in 0..k {
    //                 ans *= a[n - i - 1];
    //                 ans = (ans + 55 * MOD) % MOD;
    //             }
    //             println!("{}", ans);
    //             return;
    //         }
    //     }
    // }
}
const MOD: i64 = 1000000007;

const INF: i64 = 1 << 62;