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

public class Main {
    public static void main(String[] args) throws IOException {
        PrintWriter out = new PrintWriter(System.out);
        //Scanner sc = new Scanner();
        Reader in = new Reader();
        Main solver = new Main();
        solver.solve(out, in);
        out.flush();
        out.close();

    }
    
    static int maxn = (int)1e5;
    static int mod = (int)1e9+7;
    static int a[],b[],dp[][];
    static double[] p;
    static int n,k,c,x,t,ans;
    static long m,arr[];
    
    void solve(PrintWriter out, Reader in) throws IOException{   
        n = in.nextInt();
        k = in.nextInt();
        
        arr = new long[2*maxn+5];
        
        int temp,min=Integer.MAX_VALUE,max=0;
        for(int i=0;i<n;i++) {
            temp = in.nextInt();
            arr[temp]++;
            min = Math.min(min,temp);
            max = Math.max(max,temp);
        }
        
        for(int i=max;i>=1;i--){
            arr[i] = arr[i+1]+arr[i];
        }
        
        for(int i=2;i<=max;i++){
            arr[i] = arr[i]+arr[i-1];
        }

        int cnt = max,ans=0;

        while(cnt>min){
            cnt = bs(cnt);
            ans++;
        }
        
        out.println(ans);
    }
    
    
    static int bs(int cnt){
    	int lo=0, hi=cnt, res=-1, mid,temp=0;

            while(lo <= hi){
                mid = (lo+hi)/2;
                if(arr[cnt]-arr[mid]<=k) { hi = mid -1; res = mid; }
                else { lo = mid +1; }
            }
        ans = res;
        return res;
    }
    
    static boolean check(int d){
        long sum=0L;
        for(int i=0 ;i<n;i++) {
            if(arr[i]>=d)    sum+=arr[i]-d;
            else return false;
        }
        return sum>=k;
    }
 
    
    
    static class Reader {
 
        private InputStream mIs;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
     
        public Reader() {
            this(System.in);
        }
     
        public Reader(InputStream is) {
            mIs = is;
        }
     
        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
        
        }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = mIs.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 next() {
            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 boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
 
    }
}