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.util.*;
import java.text.*;
import java.lang.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.regex.*;
public class Main {
         public static ArrayList a[]=new ArrayList[300001];
		/*static long s[];
        static long[] seg=new long[4000000];
        static pair[] seg1=new pair[4000000];
        static long[] maxi=new long[4000000];
        static void build(int node,int start,int end) {
        	if(start==end) {
        		seg[node]=s[start];
        		return ;
        	}
        	int mid=(start+end)/2;
        	build(2*node+1,start,mid);
        	build(2*node+2,mid+1,end);
        	seg[node]=GCD(seg[2*node+1],seg[2*node+2]);
        }
        static void build1(int node,int start,int end) {
        	if(start==end) {
        		seg1[node]=new pair(s[start],1);
        		return ;
        	}
        	int mid=(start+end)/2;
        	build1(2*node+1,start,mid);
        	build1(2*node+2,mid+1,end);
        	if(seg1[2*node+1].x==seg1[2*node+2].x) {
        		seg1[node]=new pair(seg1[2*node+2].x,seg1[2*node+1].y+seg1[2*node+2].y);
        	}
        	else if(seg1[2*node+1].x<seg1[2*node+2].x)
        	{
        		seg1[node]=new pair(seg1[2*node+1].x,seg1[2*node+1].y);
        	}
        	else
        	{
        		seg1[node]=new pair(seg1[2*node+2].x,seg1[2*node+2].y);
        	}
        }
       /* static void update(int node,int start,int end,long l,int value) {
        	if(start==end) {
        		seg[node]+=value;
        		return ;
        	}
        	int mid=(start+end)/2;
        	if(start<=l && mid>=l)
        		update(2*node+1,start,mid,l,value);
        	else
        		update(2*node+2,mid+1,end,l,value);
        	seg[node]=seg[2*node+1]+seg[2*node+2];
        }*/
       
        /*static long query(int node,int start,int end,int l,int r) {
        	if(start>r || end<l)
        		return 0;
        	if(start>=l && end<=r)
        		return seg[node];
        	int mid=(start+end)/2;
        	return GCD(query(2*node+1,start,mid,l,r),query(2*node+2,mid+1,end,l,r));
        }
        static pair query1(int node,int start,int end,int l,int r) {
        	if(start>r || end<l)
        		return new pair(Long.MAX_VALUE,0);
        	if(start>=l && end<=r)
        		return seg1[node];
        	int mid=(start+end)/2;
        	pair p=query1(2*node+1,start,mid,l,r);
        	pair p1=query1(2*node+2,mid+1,end,l,r);
        	if(p.x==p1.x) {
        		return(new  pair(p.x,p.y+p1.y));
        	}
        	else if(p.x<p1.x)
        	{
        		return(p);
        	}
        	else
        	{
        		return(p1);
        	}
        }*/

		public static void main(String[] args) 
        {
            InputReader in = new InputReader(System.in);
            PrintWriter pw = new PrintWriter(System.out);
            int n=in.nextInt();
            long k=in.nextLong();
            long pre[]=new long [200005];
            int freq[]=new int[200005];
           int a[]=new int [n];
           int mini=Integer.MAX_VALUE;
           int maxi=Integer.MIN_VALUE;
            for(int i=0;i<n;i++) {
            	a[i]=in.nextInt();
            	maxi=Math.max(maxi, a[i]);
            	mini=Math.min(a[i], mini);
            	freq[a[i]]++;
            }
            for(int i=(int) maxi;i>=0;i--) {
            	pre[i]+=(freq[i]+pre[i+1]);
            }
            for(int i=(int) maxi;i>=0;i--) {
            	pre[i]+=pre[i+1];
            }
            int ans=maxi+1;
            int cnt=0;
            while(true) {
            	int start=mini;
            	int end=ans-1;
            	int temp=-1;
            	if(ans<=mini+1) {
            		break;
            	}
            	while(start<=end) {
            		int mid=(start+end)/2;
            		if(pre[mid]-pre[ans]<=k)
            		{
            			end=mid-1;
            			temp=mid;
            		}
            		else
            			start=mid+1;
            	}
            	cnt++;
            	ans=temp;
            	if(ans<=mini+1) {
            		break;
            	}
            	
            }
            pw.println(cnt);
            pw.flush();
            pw.close();
        
        
        }
		private static void debug(Object... o) {
			System.out.println(Arrays.deepToString(o));
		}
        static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        {
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
        static class tri implements Comparable<tri> {
            int p, c, l;
 
            tri(int p, int c, int l) {
                this.p = p;
                this.c = c;
                this.l = l;
            }
 
            public int compareTo(tri o) {
                return Integer.compare(l, o.l);
            }
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
        public static long mod = 1000000007;
        public static int d;
        public static int p;
        public static int q;
        
        public static int[] suffle(int[] a,Random gen)
        {
            int n = a.length;
            for(int i=0;i<n;i++)
            {
                int ind = gen.nextInt(n-i)+i;
                int temp = a[ind];
                a[ind] = a[i];
                a[i] = temp;
            }
            return a;
        }
        
        public static void swap(int a, int b){
            int temp = a;
            a = b;
            b = temp;
        }
        
        public static HashSet<Integer> primeFactorization(int n)
        {
            HashSet<Integer> a =new HashSet<Integer>();
            for(int i=2;i*i<=n;i++)
            {
                while(n%i==0)
                {
                    a.add(i);
                    n/=i;
                }
            }
            if(n!=1)
                a.add(n);
            return a;
        }
        
        public static void sieve(boolean[] isPrime,int n)
        {
            for(int i=1;i<n;i++)
                isPrime[i] = true;
            
            isPrime[0] = false;
            isPrime[1] = false;
            
            for(int i=2;i*i<n;i++)
            {
                if(isPrime[i] == true)
                {
                    for(int j=(2*i);j<n;j+=i)
                        isPrime[j] = false;
                }
            }
        }
        
        public static int GCD(int a,int b)
        {
            if(b==0)
                return a;
            else
                return GCD(b,a%b);
        }
        
        public static long GCD(long a,long b)
        {
            if(b==0)
                return a;
            else
                return GCD(b,a%b);
        }
        
        public static void extendedEuclid(int A,int B)
        {
            if(B==0)
            {
                d = A;
                p = 1 ;
                q = 0;
            }
            else
            {
                extendedEuclid(B, A%B);
                int temp = p;
                p = q;
                q = temp - (A/B)*q;
            }
        }
        
        public static long LCM(long a,long b)
        {
            return (a*b)/GCD(a,b);
        }
        
        public static int LCM(int a,int b)
        {
            return (a*b)/GCD(a,b);
        }
        
        public static int binaryExponentiation(int x,int n)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static long binaryExponentiation(long x,long n)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static int modularExponentiation(int x,int n,int M)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result * x)%M;
                x=(x%M*x)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modularExponentiation(long x,long n,long M)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result%M * x%M)%M;
                x=(x%M * x%M)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modInverse(int A,int M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static long modInverse(long A,long M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static boolean isPrime(int n)
        {
            
            if (n <= 1)  return false;
            if (n <= 3)  return true;
            
            if (n%2 == 0 || n%3 == 0) 
                return false;
         
            for (int i=5; i*i<=n; i=i+6)
            {
                if (n%i == 0 || n%(i+2) == 0)
                   return false;
            }
            
            return true;
        }
        
         public static long[] shuffle(long[] a, Random gen){ 
                for(int i = 0, n = a.length;i < n;i++){ 
                    int ind = gen.nextInt(n-i)+i; 
                    long d = a[i]; 
                    a[i] = a[ind]; 
                    a[ind] = d; 
                } 
                return a; 
            }
        static class pair implements Comparable<pair>
        {
            Long x;
            Long y;
            pair(long a,long sum)
            {
                this.x=a;
                this.y=sum;
            }
 

 
 
 
 
 
        public int compareTo(pair o) {
                int result = x.compareTo(o.x);
                if(result==0)
                    result = y.compareTo(o.y);
                
            return result;
            }  
            
            public String toString()
            {
                return x+" "+y;
            }
            
            public boolean equals(Object o)
            {
                if (o instanceof pair)
                {
                    pair p = (pair)o;
                    return p.x == x && p.y == y ;
                }
                return false;
            }
            
            public int hashCode()
            {
                return new Long(x).hashCode()*31 + new Long(y).hashCode();
            }
        }
       
 
      
}