Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

4 4
1 4
3 3
6 2
8 1

Sample Output 1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).

Its area is (8-1) × (4-1) = 21.

Sample Input 2

4 2
0 0
1 1
2 2
3 3

Sample Output 2

1

Sample Input 3

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

Sample Output 3

3999999996000000001

Watch out for integer overflows.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FasterScanner in = new FasterScanner(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, FasterScanner in, PrintWriter out) {
            final int n = in.nextInt();
            final int 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();
            }
            Arrays.sort(x);
            Arrays.sort(y);
            long ans = Long.MAX_VALUE;

            long xMin, yMin, xMax, yMax;
            for (int i = 0; i < n; i++) {
                xMin = x[i];
                for (int j = i; j < n; j++) {
                    xMax = x[j];
                    for (int o = 0; o < n; o++) {
                        yMin = y[o];
                        for (int l = o; l < n; l++) {
                            yMax = y[l];
                            int count = 0;
                            for (int m = 0; m < n; m++) {
                                if (x[m] >= xMin && x[m] <= xMax && y[m] >= yMin && y[m] <= yMax) count++;
                            }
                            if (count >= k) {
                                long s = (xMax - xMin) * (yMax - yMin);
                                if (s < ans) ans = s;
                            }
                        }
                    }
                }
            }
            out.println(ans);
        }

    }

    static class FasterScanner {
        private InputStream in;
        private byte[] buffer;
        private int bufPointer;
        private int bufLength;

        public FasterScanner(InputStream in) {
            this.in = in;
            buffer = new byte[1024];
        }

        private boolean hasNextByte() {
            if (bufPointer < bufLength) return true;
            bufPointer = 0;
            try {
                bufLength = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            return (bufLength > 0);
        }

        private int readByte() {
            if (hasNextByte()) return buffer[bufPointer++];
            return -1;
        }

        private static boolean isPrintableChar(int c) {
            return (c >= 33 && c <= 126);
        }

        public boolean hasNext() {
            while (hasNextByte() && !isPrintableChar(buffer[bufPointer])) bufPointer++;
            return hasNextByte();
        }

        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }

        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || b > '9') throw new NumberFormatException();

            while (true) {
                if (b >= '0' && b <= '9') {
                    n *= 10;
                    n += b - '0';
                } else if (b == -1 || !isPrintableChar(b)) {
                    return minus ? -n : n;
                } else {
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }

    }
}