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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int K = Integer.parseInt(sc.next());
        long INF = 5_000_000_000_000_000_000L;
        ArrayList<int[]> point_x = new ArrayList<int[]>();
        Comparator<int[]> comparator_x = new Comparator<int[]>() {
            @Override
            public int compare(int[] o1, int[] o2) {
                return Integer.compare(o1[0], o2[0]);
            }
        };
        Comparator<int[]> comparator_y = new Comparator<int[]>() {
            @Override
            public int compare(int[] o1, int[] o2) {
                return Integer.compare(o1[1], o2[1]);
            }
        };
        for (int i=0;i<N;i++) {
            int x = Integer.parseInt(sc.next());
            int y = Integer.parseInt(sc.next());
            int[] add = {x, y, i};
            point_x.add(add);
        }
        ArrayList<int[]> point_y = new ArrayList<int[]>(point_x);
        Collections.sort(point_x, comparator_x);
        Collections.sort(point_y, comparator_y);
        // for (int[] array : point_x) {
        //     System.out.println("x " + Arrays.toString(array));
        // }
        // for (int[] array : point_y) {
        //     System.out.println("y " + Arrays.toString(array));
        // }
        long ans = INF;
        for (int wid=2;wid<=N;wid++) {
            for (int i=0;i+wid<=N;i++) {
                int[] flag = new int[N];
                for (int j=i;j<i+wid;j++) {
                    flag[point_x.get(j)[2]]=1;
                }
                for (int wid_2=2;wid_2<=N;wid_2++) {
                    for (int j=0;j+wid_2<=N;j++) {
                        int cnt=0;
                        for (int k=j;k<j+wid_2;k++) {
                            // System.out.println("k wid " + k + " " + wid);
                            if (flag[point_y.get(k)[2]]==1) {
                                cnt++;
                            }
                        }
                        if (cnt>=K) {
                            ans = Math.min(ans, (long)(point_x.get(i+wid-1)[0]-point_x.get(i)[0])*(point_y.get(j+wid_2-1)[1]-point_y.get(j)[1]));
                        }
                    }
                }
            }
        }
        System.out.println(ans);
    }
}