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: Time Limit Exceeded)

use proconio::input;
#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars};
#[allow(unused_imports)]
use std::cmp::{min, max};

const INF: usize = 9999999999999999999;

fn proc_r(index: usize, v: &mut Vec<usize>, x: &Vec<usize>, y: &Vec<usize>, n: usize, k: usize) -> usize {
	if index >= n {
		if v.len() < k {
			return INF;
		}

		let mut xmin = INF;
		let mut xmax = 0;
		let mut ymin = INF;
		let mut ymax = 0;
		for i in 0..v.len() {
			xmin = min(xmin, x[v[i]]);
			xmax = max(xmax, x[v[i]]);
			ymin = min(ymin, y[v[i]]);
			ymax = max(ymax, y[v[i]]);
		}
		let ans = (xmax-xmin)*(ymax-ymin);
		if ans == 0 {
			return INF;
		}
		else {
			return ans;
		}
	}
	// 使う
	v.push(index);
	let ans1 = proc_r(index+1, v, x, y, n, k);
	v.pop();

	// 使わない
	let ans2 = proc_r(index+1, v, x, y, n, k);

	return min(ans1, ans2);
}

fn main() {
	input! {
		n: usize,
		k: usize,
		sxy: [(isize, isize); n],
	}

	let mut x = vec![0usize; n];
	let mut y = vec![0usize; n];
	for i in 0..n {
		x[i] = (sxy[i].0 + 1000000000) as usize;
		y[i] = (sxy[i].1 + 1000000000) as usize;
	}

	let mut v: Vec<usize> = vec![];
	let ans = proc_r(0, &mut v, &x, &y, n, k);
	println!("{}", ans);
}