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 proconio::input;

fn main() {
  input! {
    N: usize,
    K: usize,
    mut A: [i64;N]
  }
  let Mod = 10i64.pow(9) + 7;
  
  let mut minus_num = 0;
  let mut A: Vec<(i64, bool)> = A.into_iter().map(|v| { 
    let is_minus = v < 0;
    if is_minus {
      minus_num += 1;
    }
    (v.abs(), v < 0)
  }).collect();
  A.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap());
  
  if minus_num == N && K % 2 == 1 {
    let mut val = 1;
    for i in 0..K {
      val = (val * A[i].0);
    }
	if val < Mod {
    	println!("{}", Mod - val);
    } else {
    	println!("{}", val % Mod);
    }
    return
  }
  
  let mut can_select_minus_count = if minus_num % 2 == 1 {
    minus_num - 1
  } else {
    minus_num
  };
  
//  dbg!(can_select_minus_count, &A);
  let mut index = N - 1;
  let mut stack = Vec::with_capacity(K);
  let mut lefts = vec![];
  while 0 <= index {
  	let (next_val, minus) = A[index];
    if minus {
      can_select_minus_count -= 1;
    }
//    dbg!(next_val, minus, can_select_minus_count);
    
    if can_select_minus_count < 0 {
      lefts.push(next_val);
      continue;
    }
    
    stack.push(next_val);
    if stack.len() == K {
//      dbg!(&stack);
      if can_select_minus_count % 2 == 1 {
        lefts.push(stack.pop().unwrap());
      } else {
        let mut val = 1;
        for v in stack {
          val = (val * v) % Mod;
        }
        println!("{}", val % Mod);
        return
      }
    }
    index -= 1;
  }
}