Problem:
Score : 300 points

Problem Statement

There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.

On this sequence, Snuke can perform the following operation:

Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.

Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times.
Find the minimum number of operations required.
It can be proved that, Under the constraints of this problem, this objective is always achievable.

Constraints

2 \leq K \leq N \leq 100000

A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 ... A_N

Output

Print the minimum number of operations required.

Sample Input 1

4 3
2 3 1 4

Sample Output 1

2

One optimal strategy is as follows:

In the first operation, choose the first, second and third elements. The sequence A becomes 1, 1, 1, 4.

In the second operation, choose the second, third and fourth elements. The sequence A becomes 1, 1, 1, 1.

Sample Input 2

3 3
1 2 3

Sample Output 2

1

Sample Input 3

8 3
7 3 1 8 4 6 2 5

Sample Output 3

4

Solution in Kotlin (1.0.0) (judge verdict: Wrong Answer)

fun main(args: Array<String>) {
    val (n, k) = readLine()!!.split(" ").map { it.toInt() }
    val inputs = readLine()!!.split(" ").map { it.toInt() }

    // k 個のブロックの中に１を入れて左右に広げていく
    // 1 が入っているブロックが端にある場合

    var flag = false
    for (i in 0..k - 1) {
        if (inputs[i] == 1) {
            flag = true
        }
    }
    for (i in n - k until n) {
        if (inputs[i] == 1) {
            flag = true
        }
    }

    if (flag) {
        // 
        println(Math.ceil(n.toDouble() / (k - 1)).toInt())
        return
    }

    // 1 が入っているブロックが内部にある場合
    // -> そこで配列を２つに分割してそれぞれを端から塗っていく場合を考える
    var index = 0
    for (i in 0 until n) {
        if (inputs[i] == 1) {
            index = i
        }
    }


    // 左側残りをまず塗る( １はブロック内の右端に寄せると仮定）
    var restL = (index + 1 - k)
    var restR = n - (index + 1)
    println((Math.ceil(restL.toDouble()/(k-1)) + Math.ceil(restR.toDouble()/(k-1))).toInt())
}