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.lang.reflect.Array;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(final String[] args) {
        final Scanner scanner = new Scanner(System.in);
        final int n = scanner.nextInt();
        final int k = scanner.nextInt();

        final long[] verticals = new long[n];
        final long[] horizontals = new long[n];
        final Point[] points = new Point[n];
        for (int i = 0; i < n; i++) {
            final int x = scanner.nextInt();
            verticals[i] = x;
            final int y = scanner.nextInt();
            horizontals[i] = y;
            points[i] = new Point(x, y);
        }

        Arrays.sort(verticals);
        Arrays.sort(horizontals);
        long answer = Long.MAX_VALUE;
        for (int top = n - 1; top > 0; top--) {
            for (int bottom = 0; bottom < top; bottom++) {
                for (int right = n - 1; right > 0; right--) {
                    for (int left = 0; left < right; left++) {
                        int counter = 0;
                        for (final Point point : points) {
                            if (point.x >= verticals[left] && point.x <= verticals[right] && point.y >= horizontals[bottom] && point.y <= horizontals[top]) {
                                counter++;
                            }
                        }
                        if (counter >= k) {
                            answer = Math.min(answer, (verticals[right] - verticals[left]) * (horizontals[top] - horizontals[bottom]));
                        }
                    }
                }
            }
        }
        System.out.println(answer);
    }

    static class Point {
        int x;
        int y;

        Point(final int x, final int y) {
            this.x = x;
            this.y = y;
        }
    }
}