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.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    FastScanner in = new FastScanner(System.in);
    PrintWriter out = new PrintWriter(System.out);

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

        int[] sortedX = Arrays.copyOf(x, N);
        int[] sortedY = Arrays.copyOf(y, N);
        Arrays.sort(sortedX);
        Arrays.sort(sortedY);

        long res = Long.MAX_VALUE;
        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++) {
                int xl = sortedX[xi], xr = sortedX[xj];
                int yd = sortedY[yi], yu = sortedY[yj];
                long area = calcArea(xl, xr, yd, yu);
                int cnt = 0;
                for (int i = 0; i < N; i++) {
                    if (xl <= x[i] && x[i] <= xr && yd <= y[i] && y[i] <= yu) {
                        // System.out.println(xl + " " + xr + " " + yd + " " + yu + " : " + area);
                        cnt++;
                    }
                }
                if (area != 0 && cnt == K) {
                    res = Math.min(res, area);
                }
            }
        }
        System.out.println(res);
    }

    private long calcArea(int xl, int xr, int yd, int yu) {
        return (long) Math.abs(xr - xl) * Math.abs(yu - yd);
    }

    public static void main(String[] args) {
        new Main().run();
    }

    class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public FastScanner(InputStream stream) {
            this.stream = stream;
            //stream = new FileInputStream(new File("dec.in"));

        }

        int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        boolean isEndline(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) {
            return nextIntArray(n, 0);
        }

        int[] nextIntArray(int n, int margin) {
            int[] array = new int[n + margin];
            for (int i = 0; i < n; i++)
                array[i + margin] = nextInt();

            return array;
        }

        int[][] nextIntMap(int n, int m) {
            int[][] map = new int[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextIntArray(m);
            }
            return map;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        long[] nextLongArray(int n) {
            return nextLongArray(n, 0);
        }

        long[] nextLongArray(int n, int margin) {
            long[] array = new long[n + margin];
            for (int i = 0; i < n; i++)
                array[i + margin] = nextLong();

            return array;
        }

        long[][] nextLongMap(int n, int m) {
            long[][] map = new long[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextLongArray(m);
            }
            return map;
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        double[] nextDoubleArray(int n) {
            return nextDoubleArray(n, 0);
        }

        double[] nextDoubleArray(int n, int margin) {
            double[] array = new double[n + margin];
            for (int i = 0; i < n; i++)
                array[i + margin] = nextDouble();

            return array;
        }

        double[][] nextDoubleMap(int n, int m) {
            double[][] map = new double[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextDoubleArray(m);
            }
            return map;
        }

        String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        String[] nextStringArray(int n) {
            String[] array = new String[n];
            for (int i = 0; i < n; i++)
                array[i] = next();

            return array;
        }

        String nextLine() {
            int c = read();
            while (isEndline(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndline(c));
            return res.toString();
        }
    }
}