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.*;
import java.math.*;
import java.util.*;

public class MakeItEqual {
    private static final int TALL = 200002;

    public static void solve(FastIO io) {
        int N = io.nextInt();
        int K = io.nextInt();
        int[] H = io.nextIntArray(N);

        int req = TALL;
        int[] F = new int[TALL];
        for (int h : H) {
            --F[h + 1];
            req = Math.min(req, h);
        }
        F[0] = N;
        for (int i = 1; i < TALL; ++i) {
            F[i] += F[i - 1];
        }

        int slices = 0;
        int curr = 0;
        for (int i = TALL - 1; i > req; --i) {
            if (curr + F[i] > K) {
                ++slices;
                curr = 0;
            }
            curr += F[i];
        }
        slices += Math.min(curr, 1);
        io.println(slices);
    }

    public static class FastIO {
        private InputStream reader;
        private PrintWriter writer;

        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public FastIO(InputStream r, OutputStream w) {
            reader = r;
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(w)));
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = reader.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            return nextIntArray(n, 0);
        }

        public int[] nextIntArray(int n, int off) {
            int[] arr = new int[n + off];
            for (int i = 0; i < n; i++) {
                arr[i + off] = nextInt();
            }
            return arr;
        }

        public long[] nextLongArray(int n) {
            return nextLongArray(n, 0);
        }

        public long[] nextLongArray(int n, int off) {
            long[] arr = new long[n + off];
            for (int i = 0; i < n; i++) {
                arr[i + off] = nextLong();
            }
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

        public void printArray(int[] arr) {
            for (int i = 0; i < arr.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(arr[i]);
            }
        }

        public void printArray(long[] arr) {
            for (int i = 0; i < arr.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(arr[i]);
            }
        }

        public void printlnArray(int[] arr) {
            printArray(arr);
            writer.println();
        }

        public void printlnArray(long[] arr) {
            printArray(arr);
            writer.println();
        }

        public void printf(String format, Object... args) {
            print(String.format(format, args));
        }

        public void flush() {
            writer.flush();
        }
    }

    public static void main(String[] args) {
        FastIO io = new FastIO(System.in, System.out);
        solve(io);
        io.flush();
    }
}
