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;

public class Main {

    public static void main(String args[]) {
        try (Scanner in = new Scanner(System.in)) {

            int N = in.nextInt();
            int K = in.nextInt();

            long[] x = new long[N];
            long[] y = new long[N];
            for (int i = 0; i < N; i++) {
                x[i] = in.nextInt();
                y[i] = in.nextInt();
            }

            long[] x2 = Arrays.copyOf(x, N);
            Arrays.sort(x2);
            long[] y2 = Arrays.copyOf(y, N);
            Arrays.sort(y2);

            long area = Long.MAX_VALUE;
            for (int i = 0; i < N; i++) {
                for (int i2 = K - 1; i2 < N; i2++) {
                    for (int j = 0; j < N; j++) {
                        for (int j2 = K - 1; j2 < N; j2++) {

                            int count = 0;
                            for (int k = 0; k < N; k++) {
                                if (isInside(x2[i], y2[j], x2[i2], y2[j2], x[k], y[k])) {
                                    count++;
                                    if (count >= K) {
                                        break;
                                    }
                                }
                            }
                            if (count >= K) {
                                area = Math.min(area, Math.abs(x2[i] - x2[i2]) * Math.abs(y2[j] - y2[j2]));
                            }
                        }
                    }
                }
            }

            System.out.println(area);
        }
    }

    private static boolean isInside(long xi, long yi, long xj, long yj, long xk, long yk) {
        if (xk < Math.min(xi, xj) || xk > Math.max(xi, xj)) {
            return false;
        }
        if (yk < Math.min(yi, yj) || yk > Math.max(yi, yj)) {
            return false;
        }
        return true;
    }
}