Problem:
Score : 400 points

Problem Statement

We have N points in a two-dimensional plane.

The coordinates of the i-th point (1 \leq i \leq N) are (x_i,y_i).

Let us consider a rectangle whose sides are parallel to the coordinate axes that contains K or more of the N points in its interior.

Here, points on the sides of the rectangle are considered to be in the interior.

Find the minimum possible area of such a rectangle.

Constraints

2 \leq K \leq N \leq 50

-10^9 \leq x_i,y_i \leq 10^9 (1 \leq i \leq N)

x_i≠x_j (1 \leq i<j \leq N)

y_i≠y_j (1 \leq i<j \leq N)

All input values are integers. (Added at 21:50 JST)

Input

Input is given from Standard Input in the following format:

N K
x_1 y_1
:
x_{N} y_{N}

Output

Print the minimum possible area of a rectangle that satisfies the condition.

Sample Input 1

4 4
1 4
3 3
6 2
8 1

Sample Output 1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).

Its area is (8-1) × (4-1) = 21.

Sample Input 2

4 2
0 0
1 1
2 2
3 3

Sample Output 2

1

Sample Input 3

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

Sample Output 3

3999999996000000001

Watch out for integer overflows.

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::str::FromStr;
use std::fmt::Debug;
use std::cmp;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn main(){
    let line = read_as_vec::<usize>();
    let (n, k) = (line[0], line[1]);

    let mut points: Vec<(i64, i64)> = vec![];

    for _ in 0..n{
        let line = read_as_vec::<i64>();
        let (x, y) = (line[0], line[1]);
        points.push((x, y));
    }

    //choose 2 on vertical line
    let mut ans = std::i64::MAX;
    for x1 in 0..n{
        for x2 in x1..n{
            let right = cmp::max(points[x1].0, points[x2].0);
            let left = cmp::min(points[x1].0, points[x2].0);

            for y1 in 0..n{
                for y2 in y1..n{
                    let upper = cmp::max(points[y1].1, points[y2].1);
                    let lower = cmp::min(points[y1].1, points[y2].1);

                    let mut k_counter = 0;
                    for &(x, y) in &points{
                        if x <= right && x >= left
                            && y <= upper && y >= lower{
                                k_counter += 1;
                        }
                    }

                    if k_counter >= k{
                        ans = cmp::min(ans, (right-left)*(upper-lower));
                    }
                }
            }
        }
    }
    println!("{}", ans);
}