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: Accepted)

fun main(arg: Array<String>) {
    val (N, K) = listOfInt()
    val XY = Array(N) { listOfLong() }
    val X = XY.map { it[0] }.sorted().toLongArray()
    val Y = XY.map { it[1] }.sorted().toLongArray()
    var ans = (X.last() - X.first()) * (Y.last() - Y.first())
    for (xi in 0 until N) for (xj in xi + 1 until N)
        for (yi in 0 until N) for (yj in yi + 1 until N) {
            var count = 0
            val lx = X[xi]
            val rx = X[xj]
            val by = Y[yi]
            val uy = Y[yj]
            for (i in 0 until N) {
                if (lx <= XY[i][0] && XY[i][0] <= rx && by <= XY[i][1] && XY[i][1] <= uy) count += 1
            }
            if (count >= K) ans = Math.min(ans, (rx - lx) * (uy - by))
        }
    println(ans)
}

fun next() = readLine()!!
fun nextInt(delta: Int = 0) = Integer.parseInt(next()) + delta
fun listOfString() = next().split(" ")
fun listOfInt(d: Int = 0) = listOfString().map { Integer.parseInt(it) + d }
fun listOfLong() = listOfString().map(String::toLong)
fun listOfDouble() = listOfString().map { it.toDouble() }