There is a toy building consisting of n towers. Each tower consists of several cubes standing on each other. The i-th tower consists of h_i cubes, so it has height h_i.

Let's define operation slice on some height H as following: for each tower i, if its height is greater than H, then remove some top cubes to make tower's height equal to H. Cost of one "slice" equals to the total number of removed cubes from all towers.

Let's name slice as good one if its cost is lower or equal to k (k ≥ n).

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Calculate the minimum number of good slices you have to do to make all towers have the same height. Of course, it is always possible to make it so.

Input

The first line contains two integers n and k (1 ≤ n ≤ 2 ⋅ 10^5, n ≤ k ≤ 10^9) — the number of towers and the restriction on slices, respectively.

The second line contains n space separated integers h_1, h_2, ..., h_n (1 ≤ h_i ≤ 2 ⋅ 10^5) — the initial heights of towers.

Output

Print one integer — the minimum number of good slices you have to do to make all towers have the same heigth.

Examples

Input

5 5
3 1 2 2 4


Output

2


Input

4 5
2 3 4 5


Output

2

Note

In the first example it's optimal to make 2 slices. The first slice is on height 2 (its cost is 3), and the second one is on height 1 (its cost is 4).
import java.io.*;
import java.util.*; // тут лежат все коллекции, Random

// имя начинается с двух подчеркиваний, чтобы был первым в списке (он сортится по алфавиту)
public class __Solution {

    // определяет, запускается решение "дома" или на CF/timus
    static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    public static void main(String[] args) {
        new __Solution().run();
    }

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok;

    void init() throws FileNotFoundException {
        // иницилизация потоков вводилок/выводилок
        // System.in/System.out - стандартные потоки ввода/вывода на консоль

        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }

        tok = new StringTokenizer("");
    }

    void run() {
        try {
            long timeStart = System.currentTimeMillis();

            init();
            solve();

            out.close();

            long timeEnd = System.currentTimeMillis();
            System.err.println("Time = " + (timeEnd - timeStart));
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    // чтение строки вернет null, если ничего не осталось
    String readLine() throws IOException {
        return in.readLine();
    }

    // содержит символы, являющиеся "разделителями ввода"
    // по умолчанию это пробел (перевод строки автоматом учитывается)
    String delimiter = " ";

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine) return null;

            tok = new StringTokenizer(nextLine);
        }

        return tok.nextToken(delimiter);
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    // тут мы будем писать основное решение
    void solve() throws IOException {
        int n = readInt();
        long k = readLong();
        int[] h = new int[n];
        int max = Integer.MIN_VALUE;
        int min = Integer.MAX_VALUE;
        for (int i = 0; i < n; i++) {
            h[i] = readInt();
            if (h[i] < min)
                min = h[i];
            if (h[i] > max)
                max = h[i];
        }
        int[] p = new int[max];
        for (int i = 0; i < n; i++) {
            p[h[i] - 1]++;
        }
        for (int i = max - 2; i >= 0; i--) {
            p[i] += p[i+1];
        }
        int answer = 0;
        int i = max;
        while(i > min){
            long sum = 0;
            int l = i;
            while(sum <= k && l >= min){
                l--;
                sum += p[l];

            }
            if (sum > k)
                l++;
            i = l;
            answer++;
        }
        out.println(answer);
    }
}

