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).
//package math_codet;

import java.io.*;
import java.util.*;
 /******************************************
*    AUTHOR:         AMAN KUMAR SINGH       *
*    INSTITUITION:   KALYANI GOVERNMENT ENGINEERING COLLEGE  *
******************************************/
public class lets_do {
    InputReader in;
    PrintWriter out;
    Helper_class h;
    final long mod = 1000000007;
    public static void main(String[] args) throws java.lang.Exception{
        new lets_do().run();
    }
    void run() throws Exception{
        in=new InputReader();
        out = new PrintWriter(System.out);
        h = new Helper_class();
        int t = 1;
        while(t-->0)
            solve();
        out.flush();    
        out.close();
    }
    void solve(){
        int n = h.ni();
        long k = h.nl();
        int[] arr = new int[n];
        long[] height = new long[200005];
        int i = 0;
        int min = Integer.MAX_VALUE;
        int max = 0;
        long sum = 0;
        for(i = 0; i < n; i++){
            arr[i] = h.ni();
            min = Math.min(min, arr[i]);
            max = Math.max(max, arr[i]);
            height[1] += 1;
            height[arr[i] + 1] -= 1;
        }
        if(max == min) {
        	h.pn(0);
        	return;
        }
        long sum2[] = new long[200005];
        long sum1[] = new long[200005];
        for(i = 0; i <= max; i++){
            sum += height[i];
            sum2[i] = sum;
            //if(i < 50 && i >= 12)
             //h.pn(sum2[i]+" "+i);
        }
        sum = 0;
        for(i = min; i < max; i++){
            sum += sum2[i];
            sum1[i] = sum;
           // if(i >= min - 1&& i < 100)
           //h.pn(sum1[i]+" "+i);
        }
        int cnt = 0;
        sum = 0;
        for(i = max; i > min; i--) {
        	if(sum + sum2[i] > k) {
        		cnt++;
        		sum = sum2[i];
        	}
        	else {
        		sum += sum2[i];
        	}
        	//h.pn(sum);
        }
        h.pn(cnt + 1);
    }
    final Comparator<Entity> com=new Comparator<Entity>(){
        public int compare(Entity x, Entity y){
            int xx=Integer.compare(x.a, y.a);
            if(xx==0){
                int xxx=Integer.compare(x.b,y.b);
                return xxx;
            }
            else
                return xx;
        }
    };
    class Entity{
        int a;
        int b;
        Entity(int p, int q){
            a=p;
            b=q;
        }
    }
    class Helper_class{
        long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
 
        int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
        int bitcount(long n){return (n==0)?0:(1+bitcount(n&(n-1)));}
        void p(Object o){out.print(o);}
        void pn(Object o){out.println(o);}
        void pni(Object o){out.println(o);out.flush();}
        String n(){return in.next();}
        String nln(){return in.nextLine();}
        int ni(){return Integer.parseInt(in.next());}
        long nl(){return Long.parseLong(in.next());}
        double nd(){return Double.parseDouble(in.next());}

        long mul(long a,long b){
            if(a>=mod)a%=mod;
            if(b>=mod)b%=mod;
            a*=b;
            if(a>=mod)a%=mod;
            return a;
        }
        long modPow(long a, long p){
            long o = 1;
            while(p>0){
                if((p&1)==1)o = mul(o,a);
                a = mul(a,a);
                p>>=1;
            }
            return o;
        }
        long add(long a, long b){
            if(a>=mod)a%=mod;
            if(b>=mod)b%=mod;
            if(b<0)b+=mod;
            a+=b;
            if(a>=mod)a-=mod;
            return a;
        }
    }

    class InputReader{
        BufferedReader br;
        StringTokenizer st;
        public InputReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        public InputReader(String s) throws Exception{
            br = new BufferedReader(new FileReader(s));
        }
 
        String next(){
            while (st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (IOException  e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        String nextLine(){
            String str = "";
            try{
                str = br.readLine();
            }catch (IOException e){
                e.printStackTrace();
            }   
            return str;
        }
    }
}       