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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

import java.io.*
import java.util.*

val pw = PrintWriter(System.out)
const val MOD = 1000000007L
const val INF = 2147483647
const val LINF = 9223372036854775807L

fun main(args: Array<String>) {
    solve()
    pw.flush()
}

fun solve() {
    val (n, k) = nextIntList()
    val point = longAry2(n, 2)
    repeat(n) {
        val (x, y) = nextLongList()
        point[it][0] = x
        point[it][1] = y
    }
    val x = longAry(n)
    val y = longAry(n)
    for (i in 0 until n) {
        x[i] = point[i][0]
        y[i] = point[i][1]
    }
    x.sort()
    y.sort()
    var ans = LINF
    for (a in 0 until n - 1) {
        val leftX = x[a]
        for (b in 0 until n - 1) {
            val leftY = y[b]
            for (c in a + 1 until n) {
                val rightX = x[c]
                for (d in b + 1 until n) {
                    val rightY = y[d]
                    var count = 0
                    for (i in 0 until n) {
                        val nowX = point[i][0]
                        val nowY = point[i][1]
                        if (nowX in min(leftX, rightX)..max(leftX, rightX) && nowY in min(leftY, rightY)..max(leftY,rightY)) count++
                    }
                    if (count >= k) {
                        val area = abs(rightX - leftX) * abs(rightY - leftY)
                        ans = min(ans, area)
                    }
                }
            }
        }
    }

    println(ans)


}


fun println(v: String) {
    pw.println(v)
}

fun print(v: String) {
    pw.print(v)
}

fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun nextList() = next().split(" ").toMutableList()
fun nextIntList(index: Int = 0) = next().split(" ").map { it.toInt() + index }.toMutableList()
fun nextLongList(index: Long = 0L) = next().split(" ").map { it.toLong() + index }.toMutableList()
fun nextDoubleList() = next().split(" ").map { it.toDouble() }.toMutableList()

fun ary(n: Int, init: String = "") = Array(n) { init }
fun intAry(n: Int, init: Int = 0) = IntArray(n) { init }
fun longAry(n: Int, init: Long = 0L) = LongArray(n) { init }
fun doubleAry(n: Int, init: Double = 0.0) = DoubleArray(n) { init }
fun ary2(n: Int, m: Int, init: String = "") = Array(n) { Array(m) { init } }
fun intAry2(n: Int, m: Int, init: Int = 0) = Array(n) { IntArray(m) { init } }
fun longAry2(n: Int, m: Int, init: Long = 0) = Array(n) { LongArray(m) { init } }
fun doubleAry2(n: Int, m: Int, init: Double = 0.0) = Array(n) { DoubleArray(m) { init } }
fun ary3(n: Int, m: Int, k: Int, init: String = "") = Array(n) { Array(m) { Array(k) { init } } }
fun intAry3(n: Int, m: Int, k: Int, init: Int = 0) = Array(n) { Array(m) { IntArray(k) { init } } }
fun longAry3(n: Int, m: Int, k: Int, init: Long = 0L) = Array(n) { Array(m) { LongArray(k) { init } } }
fun doubleAry3(n: Int, m: Int, k: Int, init: Double = 0.0) = Array(n) { Array(m) { DoubleArray(k) { init } } }

fun abs(n: Int): Int = Math.abs(n)
fun abs(n: Long): Long = Math.abs(n)
fun abs(n: Double): Double = Math.abs(n)
fun max(a: Int = -INF, b: Int = -INF, c: Int = -INF, d: Int = -INF, e: Int = -INF): Int = listOf(a, b, c, d, e).max()!!
fun max(a: Long = -LINF, b: Long = -LINF, c: Long = -LINF, d: Long = -LINF, e: Long = -LINF): Long =
    listOf(a, b, c, d, e).max()!!.toLong()

fun min(a: Int = INF, b: Int = INF, c: Int = INF, d: Int = INF, e: Int = INF): Int = listOf(a, b, c, d, e).min()!!
fun min(a: Long = LINF, b: Long = LINF, c: Long = LINF, d: Long = LINF, e: Long = LINF): Long =
    listOf(a, b, c, d, e).min()!!.toLong()

fun gcd(a: Long, b: Long): Long = if (a % b == 0L) b else gcd(b, (a % b))
fun lcm(a: Long, b: Long): Long = a / gcd(a, b) * b