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 ) *} } ;}
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 <_ >>() } ;($next :expr ,chars ) =>{read_value !($next ,String ) .chars () .collect ::<Vec <char >>() } ;($next :expr ,usize1 ) =>{read_value !($next ,usize ) -1 } ;($next :expr ,$t :ty ) =>{$next () .parse ::<$t >() .expect ("Parse error" ) } ;}

fn main() {
   input! {
      n: usize,
      k: usize,
      _xy: [(i64, i64); n],
   }
   let mut xy = _xy;
   xy.sort();
   let mut ans = 4e18 as i64;
   for i in 0..n - 1 {
      for j in i + k - 1..n {
         let w = xy[j].0 - xy[i].0;
         let mut ys = vec![];
         for l in i..j + 1 {
            ys.push(xy[l].1);
         }
         let p = j - i + 1;
         ys.sort();
         for l in 0..p - k + 1 {
            let h = ys[l + k - 1] - ys[l];
            ans = std::cmp::min(ans, w * h);
         }
      }
   }
   println!("{}", ans);
}

/// Equivalent to std::lowerbound and std::upperbound in c++
pub trait BinarySearch<T> {
   fn lower_bound(&self, x: &T) -> usize;
   fn upper_bound(&self, x: &T) -> usize;
}
#[allow(dead_code)]
impl<T: Ord> BinarySearch<T> for [T] {
   fn lower_bound(&self, x: &T) -> usize {
      let mut low = 0;
      let mut high = self.len();
      while low != high {
         let mid = (low + high) / 2;
         match self[mid].cmp(x) {
            std::cmp::Ordering::Less => {
               low = mid + 1;
            }
            std::cmp::Ordering::Equal | std::cmp::Ordering::Greater => {
               high = mid;
            }
         }
      }
      low
   }
   fn upper_bound(&self, x: &T) -> usize {
      let mut low = 0;
      let mut high = self.len();
      while low != high {
         let mid = (low + high) / 2;
         match self[mid].cmp(x) {
            std::cmp::Ordering::Less | std::cmp::Ordering::Equal => {
               low = mid + 1;
            }
            std::cmp::Ordering::Greater => {
               high = mid;
            }
         }
      }
      low
   }
}