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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.SplittableRandom;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Pradyumn
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int n = in.nextInt();
            int K = in.nextInt();
            long[] x = new long[n];
            long[] y = new long[n];
            long[][] p = new long[n][];
            for (int i = 0; i < n; ++i) {
                p[i] = in.nextLongArray(2);
                x[i] = p[i][0];
                y[i] = p[i][1];
            }
            ArrayUtils.sort(x);
            ArrayUtils.sort(y);
            long ret = Long.MAX_VALUE;
            for (int i = 0; i < n; ++i) {
                for (int j = i + 1; j < n; ++j) {
                    for (int k = 0; k < n; ++k) {
                        for (int l = k + 1; l < n; ++l) {
                            int count = 0;
                            long x1 = x[i];
                            long x2 = x[j];
                            long y1 = y[k];
                            long y2 = y[l];

                            for (long[] v : p) {
                                long nx = v[0];
                                long ny = v[1];
                                if (x1 <= nx && nx <= x2 && y1 <= ny && ny <= y2) ++count;
                            }
                            if (count >= K) {
                                long now = (x2 - x1) * (y2 - y1);
                                ret = Math.min(ret, now);
                            }
                        }
                    }
                }
            }
            out.println(ret);
        }

    }

    static class ArrayUtils {
        public static long[] sort(long[] a) {
            a = shuffle(a, new SplittableRandom());
            Arrays.sort(a);
            return a;
        }

        public static long[] shuffle(long[] a, SplittableRandom gen) {
            for (int i = 0, n = a.length; i < n; i++) {
                int ind = gen.nextInt(n - i) + i;
                long d = a[i];
                a[i] = a[ind];
                a[ind] = d;
            }
            return a;
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

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

        public int nextInt() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = pread();
            }
            int res = 0;
            do {
                if (c == ',') {
                    c = pread();
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = pread();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextLong();
            }
            return array;
        }

        private boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

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

        private interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}