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)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String {
            bytes
                .by_ref()
                .map(|r| r.unwrap() as char)
                .skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{min, max};

fn main() {
    input!{
        n: usize,
        k: usize,
        v: [(i64, i64); n]
    }
    let (xs, ys): (Vec<i64>, Vec<i64>) = v.iter().cloned().unzip();
    let xsc = compress(&xs);
    let ysc = compress(&ys);
    let mut tab = vec![vec![0; n + 1]; n + 1];
    for i in 0..n {
        tab[xsc[i] + 1][ysc[i] + 1] += 1;
    }
    for i in 0..n {
        for j in 0..n {
            tab[i + 1][j + 1] += tab[i][j + 1] + tab[i + 1][j] - tab[i][j];
        }
    }
    let mut ans = i64::max_value();
    for i in 0..n {
        for j in i..n {
            for l in j..n {
                for m in l..n {
                    let t = vec![i, j, l, m];
                    let xl = t.iter().cloned().min_by_key(|&x| xs[x]).unwrap();
                    let yl = t.iter().cloned().min_by_key(|&x| ys[x]).unwrap();
                    let xr = t.iter().cloned().max_by_key(|&x| xs[x]).unwrap();
                    let yr = t.iter().cloned().max_by_key(|&x| ys[x]).unwrap();
                    if tab[xsc[xr] + 1][ysc[yr] + 1] + tab[xsc[xl]][ysc[yl]] - tab[xsc[xr] + 1][ysc[yl]] - tab[xsc[xl]][ysc[yr] + 1] < k {
                        continue;
                    }
                    ans = min(ans, (xs[xr] - xs[xl]) * (ys[yr] - ys[yl]));
                }
            }
        }
    }
    println!("{}", ans);
}

fn compress(v: &Vec<i64>) -> Vec<usize> {
    let mut w = v.clone();
    w.sort();
    let mut ret: Vec<usize> = vec![0; v.len()];
    for i in 0..v.len() {
        let mut l = 0;
        let mut r = w.len();
        while l + 1 < r {
            let m = (l + r) / 2;
            if w[m] > v[i] {
                r = m;
            } else {
                l = m;
            }
        }
        ret[i] = l;
    }
    ret
}