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: Wrong Answer)

use std::io::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n: usize = read();
    let k: usize = read();
    let mut xs = vec![0 as i64; n];
    let mut ys = vec![0 as i64; n];
    for i in 0..n {
        xs[i] = read();
        ys[i] = read();
    }
    let mut sorted_xs = xs.clone();
    let mut sorted_ys = ys.clone();
    sorted_xs.sort();
    sorted_ys.sort();
    let mut ans = 1i64 << 62;
    for yleft in 0..n {
        for yright in yleft + 1..n {
            let count_cnt = |xleft: usize, xright: usize| {
                let mut ret = 0;
                for i in 0..n {
                    if sorted_xs[xleft] <= xs[i] && xs[i] <= sorted_xs[xright]
                        && sorted_ys[yleft] <= ys[i]
                        && ys[i] <= sorted_ys[yright]
                    {
                        ret += 1;
                    }
                }
                ret
            };
            let mut xleft = 0;
            let mut xright = 0;
            while xright < n {
                while xright < n && count_cnt(xleft, xright) < k {
                    xright += 1;
                }
                while xright < n && xleft < xright && count_cnt(xleft, xright) > k {
                    xleft += 1;
                }
                if xright < n && count_cnt(xleft, xright) == k {
                    let area = (sorted_xs[xright] - sorted_xs[xleft])
                        * (sorted_ys[yright] - sorted_ys[yleft]);
                    ans = std::cmp::min(ans, area);
                }
                xright += 1;
            }
        }
    }
    println!("{}", ans);
}