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).

<image>

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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Queue;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Task solver = new Task();
		solver.solve(1, in, out);
		out.close();
	}

	static class Task {
		public void solve(int testNumber, InputReader in, PrintWriter out) {
			int n = in.nextInt();
			int k = in.nextInt();
			int[] v = new int[200001];
			int low = 200001;
			int high = 0;
			int[] hs = new int[n];
			for (int i = 0; i < n; i++) {
				hs[i] = in.nextInt();
			}
			Arrays.sort(hs);
			low = hs[0];
			high = hs[n - 1];
			if (low == high) {
				out.println(0);
				return;
			}
			for (int i = 1; i <= low; i++) {
				v[i] = n;
			}
			int cur = low;
			for (int i = 1; i < n; i++) {
				if (hs[i] > cur) {
					for (int j = cur + 1; j <= hs[i]; j++) {
						v[j] = (n - i);
					}
					cur = hs[i];
				}
			}
			long sum = 0;
			int count = 0;
			for (int i = high; i >= low; i--) {
				if (i == low && sum > 0) {
					count++;
					break;
				}
				if (sum + v[i] > k) {
					sum = v[i];
					count++;
				} else {
					sum += v[i];
					if (i == low) {
						count++;
					}
				}
			}
			out.println(count);
		}
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public Long nextLong() {
			return Long.parseLong(next());
		}

		public Double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}