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).
import java.io.IOException; 
import java.io.InputStream; 
import java.io.PrintWriter; 
import java.util.*; 
 

public class c{ 

	static void solve(){
		int n = ni();
		long k = nl();
		int top = 2*100000;
		long[] num = new long[top+1];
		for(int i=0;i<n;++i){
			int h = ni();
			num[h]++;
		}
		for(int i=top-1;i>=0;--i)num[i]+=num[i+1];
		int ans = 0;
		long cnt = 0;
		for(int i=top;i>=1;--i){
			if(num[i]==n)break;
			cnt+=num[i];
			if(cnt + num[i-1]>k || (num[i-1]==n&&cnt>0)){
				++ans;
				cnt=0;
			}
		}
		out.println(ans);
 
	} 
 
 
 
 
	 public static void main(String[] args){ 
		 solve(); 
		 out.flush(); 
	 } 
	 private static InputStream in = System.in; 
	 private static PrintWriter out = new PrintWriter(System.out); 
 
	 static boolean inrange(int y, int x, int h, int w){ 
		 return y>=0 && y<h && x>=0 && x<w; 
	 } 
	 @SuppressWarnings("unchecked") 
	 static<T extends Comparable> int lower_bound(List<T> list, T key){ 
		 int lower=-1;int upper=list.size(); 
		 while(upper - lower>1){ 
		 int center =(upper+lower)/2; 
		 if(list.get(center).compareTo(key)>=0)upper=center; 
		 else lower=center; 
		 } 
		 return upper; 
	 } 
	 @SuppressWarnings("unchecked") 
	 static <T extends Comparable> int upper_bound(List<T> list, T key){ 
		 int lower=-1;int upper=list.size(); 
		 while(upper-lower >1){ 
		 int center=(upper+lower)/2; 
		 if(list.get(center).compareTo(key)>0)upper=center; 
		 else lower=center; 
		 } 
		 return upper; 
	 } 
	 @SuppressWarnings("unchecked") 
	 static <T extends Comparable> boolean next_permutation(List<T> list){ 
		 int lastIndex = list.size()-2; 
		 while(lastIndex>=0 && list.get(lastIndex).compareTo(list.get(lastIndex+1))>=0)--lastIndex; 
		 if(lastIndex<0)return false; 
		 int swapIndex = list.size()-1; 
		 while(list.get(lastIndex).compareTo(list.get(swapIndex))>=0)swapIndex--; 
		 T tmp = list.get(lastIndex); 
		 list.set(lastIndex++, list.get(swapIndex)); 
		 list.set(swapIndex, tmp); 
		 swapIndex = list.size()-1; 
		 while(lastIndex<swapIndex){ 
		 tmp = list.get(lastIndex); 
		 list.set(lastIndex, list.get(swapIndex)); 
		 list.set(swapIndex, tmp); 
		 ++lastIndex;--swapIndex; 
		 } 
		 return true; 
	 } 
	 private static final byte[] buffer = new byte[1<<15]; 
	 private static int ptr = 0; 
	 private static int buflen = 0; 
	 private static boolean hasNextByte(){ 
		 if(ptr<buflen)return true; 
		 ptr = 0; 
		 try{ 
			 buflen = in.read(buffer); 
		 } catch (IOException e){ 
			 e.printStackTrace(); 
		 } 
		 return buflen>0; 
	 } 
	 private static int readByte(){ if(hasNextByte()) return buffer[ptr++]; else return -1;} 
	 private static boolean isSpaceChar(int c){ return !(33<=c && c<=126);} 
	 private static int skip(){int res; while((res=readByte())!=-1 && isSpaceChar(res)); return res;} 
 
	 private static double nd(){ return Double.parseDouble(ns()); } 
	 private static char nc(){ return (char)skip(); } 
	 private static String ns(){ 
		 StringBuilder sb = new StringBuilder(); 
		 for(int b=skip();!isSpaceChar(b);b=readByte())sb.append((char)b); 
		 return sb.toString(); 
	 } 
	 private static int[] nia(int n){ 
		 int[] res = new int[n]; 
		 for(int i=0;i<n;++i)res[i]=ni(); 
		 return res; 
	 } 
	 private static long[] nla(int n){ 
		 long[] res = new long[n]; 
		 for(int i=0;i<n;++i)res[i]=nl(); 
		 return res; 
	 } 
	 private static int ni(){ 
		 int res=0,b; 
		 boolean minus=false; 
		 while((b=readByte())!=-1 && !((b>='0'&&b<='9') || b=='-')); 
		 if(b=='-'){ 
			 minus=true; 
			 b=readByte(); 
		 } 
		 for(;'0'<=b&&b<='9';b=readByte())res=res*10+(b-'0'); 
		 return minus ? -res:res; 
	 } 
	 private static long nl(){ 
		 long res=0,b; 
		 boolean minus=false; 
		 while((b=readByte())!=-1 && !((b>='0'&&b<='9') || b=='-')); 
		 if(b=='-'){ 
			 minus=true; 
			 b=readByte(); 
		 } 
		 for(;'0'<=b&&b<='9';b=readByte())res=res*10+(b-'0'); 
		 return minus ? -res:res; 
	} 
} 

