Problem: 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.

Examples

Input

4 4
1 4
3 3
6 2
8 1


Output

21


Input

4 2
0 0
1 1
2 2
3 3


Output

1


Input

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999


Output

3999999996000000001

Solution (in JAVA):

Solution:
import java.util.Arrays;
import java.util.Scanner;
 
/**
 *http://abc075.contest.atcoder.jp/tasks/abc075_d
 */
public class Main {
 
	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		final int N = sc.nextInt();
		final int K = sc.nextInt();
		Point[] points = new Point[N];
		long[] xList = new long[N];
		long[] yList = new long[N];
		for(int i=0; i<N; i++){
			points[i] = new Point(sc.nextLong(), sc.nextLong());
			xList[i] = points[i].x;
			yList[i] = points[i].y;
		}
		sc.close();
		
		long ans = Long.MAX_VALUE;
		Arrays.sort(xList);
		Arrays.sort(yList);
		for(int xi=0; xi<N; xi++){
			for(int xj=xi+1; xj<N; xj++){
				for(int yi=0; yi<N; yi++){
					for(int yj=yi+1; yj<N; yj++){
						long xl = xList[xi];
						long xr = xList[xj];
						long yb = yList[yi];
						long yu = yList[yj];
						int num = 0;
						for(Point p:points){
							if(xl<=p.x && p.x<=xr && yb<=p.y && p.y<=yu){
								num++;
							}
						}
						if(num>=K){
							ans = Math.min(ans, (xr-xl)*(yu-yb));
						}
					}
				}
			}
		}
		System.out.println(ans);
 
	}
	
	static class Point{
		public Point(long x, long y) {
			this.x = x;
			this.y = y;
		}
		long x;
		long y;
	}
 
}