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).
/*
TO LEARN
1-segment trees
2-euler tour
*/
            import java.util.*;
		    import java.math.*;
		    import java.io.*; 
		    import java.util.stream.Collectors;
 
		     public class A{
		     
		    static FastReader scan=new FastReader();
		     public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
		     
public static long hash(String string) {
  long h = 1125899906842597L; // prime
  int len = string.length();

  for (int i = 0; i < len; i++) {
    h = 31*h + string.charAt(i);
  }
  return h;
}

		    public static void main(String[] args)  throws Exception 
		    {
		    //SUCK IT UP AND DO IT ALRIGHT
		    //scan=new FastReader("vs.txt");
		    //out = new PrintWriter("hps.out");
		 
		 

		    int tt=1;
 //tt=scan.nextInt();
	 outer:while(tt-->0)
		    {
		    	int n=scan.nextInt(),k=scan.nextInt();
		    	long arr[]=new long[n];
		    	long cnt[]=new long[(int)2e5+5];
		    	long fin=Long.MAX_VALUE,fin2=Long.MIN_VALUE;
		    	for(int i=0;i<n;i++)
		    	{
		    		arr[i]=scan.nextInt();
		    		cnt[(int)arr[i]]++;
		    		fin=Math.min(fin,arr[i]);
		    		fin2=Math.max(fin2,arr[i]);
		    	}
		    	//Arrays.sort(arr);
		    	long l=0,sum=0;
		    	long p=(long)2e5+4;
		    	long res=0;
		    	while(true)
		    	{
		    		long o=sum-l*(p);
		    		//out.println(sum+" "+o+" "+p+" "+l);
		    		if(o>k)
		    		{
		    			//out.println(o+" "+sum);
		    			res++;
		    			sum=l*(p+1);
		    			//l=l*(p+1);
		    		}
		    		sum+=(cnt[(int)p]*(p));
		    		l+=cnt[(int)p];
		    		
		    		if(p==fin)
		    			break;
		    		p--;
		    	}
		    	if(fin!=fin2)
		    		res++;
		    	out.println(res);



}
		  	    out.close();
		    }
		    static class special implements Comparable<special>{
		        int x,y;
		        String s;
		        special(int x,int y,String s)
		        {
		            this.x=x;
		           this.y=y;
		           this.s=s;
		        }
		     
		     @Override
		            public boolean equals(Object o){
		                if (o == this) return true;
		                if (o.getClass() != getClass()) return false;
		                special t = (special)o;
		                return t.x == x && t.y == y&&t.s.equals(s);
		            }
		     
		    public int compareTo(special o)
		    {
		        return Integer.compare(x,o.x);
		    }
		    }
		    static long binexp(long a,long n)
		    {
		        if(n==0)
		            return 1;
		        long res=binexp(a,n/2);
		        if(n%2==1)
		            return res*res*a;
		        else 
		            return res*res;
		    }
		     
		    static long powMod(long base, long exp, long mod) {
		           if (base == 0 || base == 1) return base;
		           if (exp == 0) return 1;
		           if (exp == 1) return (base % mod+mod)%mod;
		           long R = (powMod(base, exp/2, mod) % mod+mod)%mod;
		           R *= R;
		           R %= mod;
		           if ((exp & 1) == 1) {
		               return (base * R % mod+mod)%mod;
		           }
		           else return (R %mod+mod)%mod;
		       }
		    static double dis(double x1,double y1,double x2,double y2)
		    {
		        return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
		    }
		    static long mod(long x,long y)
		        {
		            if(x<0)
		                x=x+(-x/y+1)*y;
		            return x%y;
		        }
		     public static  long pow(long b, long e) {
		                long r = 1;
		                while (e > 0) {
		                    if (e % 2 == 1) r = r * b ;
		                    b = b * b;
		                    e >>= 1;
		                }
		                return r;
		            }
		    private static void sort(long[] arr) {
		            List<Long> list = new ArrayList<>();
		            for (long object : arr) list.add(object);
		            Collections.sort(list);
		        //Collections.reverse(list);
		            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
		        }
		    private static void sort2(int[] arr) {
		            List<Integer> list = new ArrayList<>();
		            for (int object : arr) list.add(object);
		            Collections.sort(list);
		        Collections.reverse(list);
		            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
		        }
		     public static class FastReader {
		            BufferedReader br;
		            StringTokenizer root;
		            
		     
		            public FastReader() {
		                br = new BufferedReader(new InputStreamReader(System.in));
		            }
		            FastReader(String filename)throws Exception
		            {
		     
		                br=new BufferedReader(new FileReader(filename));
		            }
		     
		            boolean hasNext(){
		                String line;
		                while(root.hasMoreTokens())
		                    return true;
		                return false;
		            }
		     
		            String next() {
		                while (root == null || !root.hasMoreTokens()) {
		                    try {
		                        root = new StringTokenizer(br.readLine());
		                    } catch (Exception addd) {
		                        addd.printStackTrace();
		                    }
		                }
		                return root.nextToken();
		            }
		     
		            int nextInt() {
		                return Integer.parseInt(next());
		            }
		     
		            double nextDouble() {
		                return Double.parseDouble(next());
		            }
		     
		            long nextLong() {
		                return Long.parseLong(next());
		            }
		     
		            String nextLine() {
		                String str = "";
		                try {
		                    str = br.readLine();
		                } catch (Exception addd) {
		                    addd.printStackTrace();
		                }
		                return str;
		            }
		             public int[] nextIntArray(int arraySize) {
		                int array[] = new int[arraySize];
		     
		                for (int i = 0; i < arraySize; i++) {
		                    array[i] = nextInt();
		                }
		     
		                return array;
		            }
		    }
		     static class Pair implements Comparable<Pair>{
		            public long x, y,z;
		            public Pair(long x1, long y1,long z1) {
		                x=x1;
		                y=y1;
		                z=z1;
		            }
		             public Pair(long x1, long y1) {
		                x=x1;
		                y=y1;
		    
		            }
		            
		            @Override
		            public int hashCode() {
		                return (int)(x + 31 * y);
		            }
		            public String toString() {
		                return x + " " + y+" "+z;
		            }
		            @Override
		            public boolean equals(Object o){
		                if (o == this) return true;
		                if (o.getClass() != getClass()) return false;
		                Pair t = (Pair)o;
		                return t.x == x && t.y == y&&t.z==z;
		            }
		    public int compareTo(Pair o)
		    {return (int)(x-o.x);
		     
		        }
		     
		    }
		     static class tuple{
		            int x,y,z;
		            tuple(int a,int b,int c){
		                x=a;
		                y=b;
		                z=c;
		            }
		        }
		        static class Edge{
		            int d,w;
		            Edge(int d,int w)
		            {
		                this.d=d;
		                this.w=w;
		            }
		        }
		    }

		     
