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 (1.42.0) (judge verdict: Accepted)

macro_rules! get {
    ($t:ty) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t:ty),*) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            (
                $(iter.next().unwrap().parse::<$t>().unwrap(),)*
            )
        }
    };
    ($t:ty; $n:expr) => {
        (0..$n).map(|_|
            get!($t)
        ).collect::<Vec<_>>()
    };
    ($($t:ty),*; $n:expr) => {
        (0..$n).map(|_|
            get!($($t),*)
        ).collect::<Vec<_>>()
    };
}

use std::cmp;

fn main() {
    let (n, k) = get!(usize, usize);
    let mut xx = Vec::new();
    let mut yy = Vec::new();
    for _ in 0..n {
        let (x, y) = get!(i64, i64);
        xx.push(x);
        yy.push(y);
    }

    let mut a = i64::max_value();
    for t in 0..n {
        for b in 0..n {
            if yy[t] - yy[b] <= 0 { continue; }
            for l in 0..n {
                for r in 0..n {
                    if xx[r] - xx[l] <= 0 { continue; }
                    let mut kk = 0;
                    for i in 0..n {
                        if yy[b] <= yy[i] && yy[i] <= yy[t] && xx[l] <= xx[i] && xx[i] <= xx[r] {
                            kk += 1;
                        }
                    }
                    if kk == k {
                        a = cmp::min(a, (yy[t] - yy[b]) * (xx[r] - xx[l]));
                    }
                }
            }
        }
    }
    println!("{}", a);
}