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)

fn get_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().to_string()
}

fn reads<T>() -> Vec<T>
    where
        T: std::str::FromStr,
        <T as std::str::FromStr>::Err: std::fmt::Debug {
    get_line().split(' ').map(|x| x.parse().unwrap()).collect()
}

fn main() {
    let nk = reads();

    let mut ps = vec![];
    for _ in 0..nk[0] {
        let xy: Vec<i64> = reads();

        ps.push((xy[0], xy[1]));
    }

    ps.sort_by(|lhs, rhs| {
        lhs.0.cmp(&rhs.0)
    });

    let mut xi = 0;
    let mut xj = 0;
    let mut res = None;
    while ps.len() > xj {
        if nk[1] > xj - xi + 1 {
            xj += 1;
        }
        else {
            let dx = ps[xj].0 - ps[xi].0;

            let mut h = ps[xi].1;
            let mut l = ps[xi].1;
            for i in xi..(xj + 1) {
                if ps[i].1 > h {
                    h = ps[i].1;
                }
                if l > ps[i].1 {
                    l = ps[i].1;
                }
            }

            let dy = h - l;
            let r = dy * dx;
            if let Some(v) = res {
                if v > r {
                    res = Some(r);
                }
            }
            else {
                res = Some(r);
            }

            xi += 1;
        }
    }

    ps.sort_by(|lhs, rhs| {
        lhs.1.cmp(&rhs.1)
    });

    xi = 0;
    xj = 0;
    while ps.len() > xj {
        if nk[1] > xj - xi + 1 {
            xj += 1;
        }
        else {
            let dx = ps[xj].1 - ps[xi].1;

            let mut h = ps[xi].0;
            let mut l = ps[xi].0;
            for i in xi..(xj + 1) {
                if ps[i].0 > h {
                    h = ps[i].0;
                }
                if l > ps[i].0 {
                    l = ps[i].0;
                }
            }

            let dy = h - l;
            let r = dy * dx;
            if let Some(v) = res {
                if v > r {
                    res = Some(r);
                }
            }
            else {
                res = Some(r);
            }

            xi += 1;
        }
    }

    println!("{}", res.unwrap());
}