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::cmp::{max, min};
use std::fs;
use std::io::{stdin, Read};

macro_rules! parse {
    ($it: ident) => {
        $it.next().unwrap().parse().unwrap()
    };
    ($it: ident,2) => {
        (parse!($it), parse!($it))
    };
    ($it: ident,3) => {
        (parse!($it), parse!($it), parse!($it))
    };
    ($it: ident,4) => {
        (parse!($it), parse!($it), parse!($it), parse!($it))
    };
    ($it: ident, $n: expr) => {
        (&mut $it).take($n).map(|e| e.parse().unwrap()).collect();
    };
}

fn solve(s: &str) {
    let mut it = s.split_whitespace();
    let (n, k): (usize, usize) = parse!(it, 2);
    let p: Vec<(i64, i64)> = (0..n).map(|_| parse!(it, 2)).collect();
    let mut cands = vec![];
    for i in 0..n {
        for j in i..n {
            if k == 2 {
                cands.push(vec![p[i], p[j]]);
                continue;
            }
            for k in j..n {
                if k == 3 {
                    cands.push(vec![p[i], p[j], p[k]]);
                    continue;
                }
                for l in k..n {
                    cands.push(vec![p[i], p[j], p[k], p[l]])
                }
            }
        }
    }

    let mut ret = std::i64::MAX;
    for ps in cands {
        let l = ps.iter().min_by_key(|x| x.0).unwrap().0;
        let r = ps.iter().max_by_key(|x| x.0).unwrap().0;
        let u = ps.iter().max_by_key(|x| x.1).unwrap().1;
        let d = ps.iter().min_by_key(|x| x.1).unwrap().1;
        let s = (r - l) * (u - d);
        if p.iter()
            .filter(|&&(x, y)| l <= x && x <= r && d <= y && y <= u)
            .count()
            >= k
        {
            ret = min(s, ret)
        }
    }
    println!("{}", ret);
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    solve(&s);
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_input() {
        let s = "
        ";
        solve(s);
    }
}