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.*;
import java.util.*;

public class Main {
    static InputStream is;
    static PrintWriter out;
    static String INPUT = "";

    static long MODULO = 1_000_000_000 + 7;
    static long[] fac = new long[200000];
    static long[] invfac = new long[200000];
    static long[] inv = new long[200000];
    
    static void solve()
    {
        int n = ni();
        int k = ni();
        int[] x = new int[n];
        int[] y = new int[n];
        for(int i = 0; i < n; i++){
            x[i] = ni();
            y[i] = ni();
        }
        Arrays.sort(x);
        Arrays.sort(y);
        long minarea = Long.MAX_VALUE;
        for(int x1 = 0; x1 < n; x1++){
            for(int x2 = x1+1; x2 < n; x2++){
                for(int y1 = 0; y1 < n; y1++){
                    for(int y2 = y1+1; y2 < n; y2++){
                        int res = 0;
                        long area = 0;
                        for(int i = 0; i < n; i++){
                            if(x[i] >= x[x1] && x[i] <= x[x2] && y[i] >= y[y1] && y[i] <= y[y2]){
                                res++;
                            }
                        }
                        if(res >= k){
                            area = (long)(x[x2]-x[x1]) * (long)(y[y2]-y[y1]);
                            if(area < minarea){
                                minarea = area;
                            }
                        }
                    }
                }
            }
        }
        out.println(minarea);

    }

    
    public static void main(String[] args) throws Exception
    {
        long S = System.currentTimeMillis();
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        
        solve();
        out.flush();
        long G = System.currentTimeMillis();
        tr(G-S+"ms");
    }

    
    private static boolean eof()
    {
        if(lenbuf == -1)return true;
        int lptr = ptrbuf;
        while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
        
        try {
            is.mark(1000);
            while(true){
                int b = is.read();
                if(b == -1){
                    is.reset();
                    return true;
                }else if(!isSpaceChar(b)){
                    is.reset();
                    return false;
                }
            }
        } catch (IOException e) {
            return true;
        }
    }
    
    private static byte[] inbuf = new byte[1024];
    static int lenbuf = 0, ptrbuf = 0;
    
    private static int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//  private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
    private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private static double nd() { return Double.parseDouble(ns()); }
    private static char nc() { return (char)skip(); }
    
    private static String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private static char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private static char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private static int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private static int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }

    private static int[] nsi(){
        char[] s = ns().toCharArray();
        int[] a = new int[s.length];
        for(int j = 0; j < s.length; j++){
           a[j] = s[j] - '0';
        }
        return a;
    }
}