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 main() {
  let (n, k): (usize, usize) = read_tuple();
  let mut xys: Vec<(i64, i64)> = read_tuples(n);
  
  xys.sort();
  let area = |xys: &[(i64,i64)]| {
    let dx = &xys.iter().map(|p|p.0).max().unwrap() - &xys.iter().map(|p|p.0).min().unwrap();
    let dy = &xys.iter().map(|p|p.1).max().unwrap() - &xys.iter().map(|p|p.1).min().unwrap();
    dx * dy
  };
  let ansx = xys.windows(k).map(area).min().unwrap();

  xys.sort_by(|p1,p2|p1.1.cmp(&p2.1));
  let area = |xys: &[(i64,i64)]| {
    let dx = &xys.iter().map(|p|p.0).max().unwrap() - &xys.iter().map(|p|p.0).min().unwrap();
    let dy = &xys.iter().map(|p|p.1).max().unwrap() - &xys.iter().map(|p|p.1).min().unwrap();
    dx * dy
  };
  let ansy = xys.windows(k).map(area).min().unwrap();

  println!("{}", std::cmp::min(ansx,ansy));
}

fn read_tuple<T1: std::str::FromStr, T2: std::str::FromStr>() -> (T1, T2) {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  let mut it = buf.trim().split_whitespace();
  let x = it.next().unwrap().parse::<T1>().ok().unwrap();
  let y = it.next().unwrap().parse::<T2>().ok().unwrap();
  (x, y)
}

fn read_tuples<T1: std::str::FromStr, T2: std::str::FromStr>(n: usize) -> Vec<(T1, T2)> {
  let mut vec: Vec<(T1, T2)> = vec![];
  for _ in 0 .. n {
    vec.push(read_tuple());
  }
  vec
}