Professor Ibrahim has prepared the final homework for his algorithm’s class. He asked his students to implement the Posterization Image Filter.

Their algorithm will be tested on an array of integers, where the i-th integer represents the color of the i-th pixel in the image. The image is in black and white, therefore the color of each pixel will be an integer between 0 and 255 (inclusive).

To implement the filter, students are required to divide the black and white color range [0, 255] into groups of consecutive colors, and select one color in each group to be the group’s key. In order to preserve image details, the size of a group must not be greater than k, and each color should belong to exactly one group.

Finally, the students will replace the color of each pixel in the array with that color’s assigned group key.

To better understand the effect, here is an image of a basking turtle where the Posterization Filter was applied with increasing k to the right. 

<image>

To make the process of checking the final answer easier, Professor Ibrahim wants students to divide the groups and assign the keys in a way that produces the lexicographically smallest possible array.

Input

The first line of input contains two integers n and k (1 ≤ n ≤ 10^5, 1 ≤ k ≤ 256), the number of pixels in the image, and the maximum size of a group, respectively.

The second line contains n integers p_1, p_2, ..., p_n (0 ≤ p_i ≤ 255), where p_i is the color of the i-th pixel.

Output

Print n space-separated integers; the lexicographically smallest possible array that represents the image after applying the Posterization filter.

Examples

Input

4 3
2 14 3 4


Output

0 12 3 3


Input

5 2
0 2 1 255 254


Output

0 1 1 254 254

Note

One possible way to group colors and assign keys for the first sample:

Color 2 belongs to the group [0,2], with group key 0.

Color 14 belongs to the group [12,14], with group key 12.

Colors 3 and 4 belong to group [3, 5], with group key 3.

Other groups won't affect the result so they are not listed here.
import java.awt.Checkbox;
import java.awt.Point;
import java.io.*;
                    import java.math.*;
                    import java.util.*;
import java.util.Map.Entry;

import javax.print.attribute.SetOfIntegerSyntax;
import javax.swing.plaf.FontUIResource;




             
                    public class CODE2{
                      private static InputStream stream;
                        private static byte[] buf = new byte[1024];
                        private static int curChar,MAX;
                        private static int numChars;
                        private static SpaceCharFilter filter;
                        private static PrintWriter pw;
                        private static long count = 0,mod=1000000007;
                        static int BIT[];
                        private static boolean primer[];
                    //    private static TreeSet<Integer> ts=new TreeSet[200000];
public final static int INF = (int) 1E9;

public static void main(String args[]) {
    InputReader(System.in);
    pw = new PrintWriter(System.out); 
    new Thread(null ,new Runnable(){
       public void run(){
           try{
               solve();
               
               pw.close();
           } catch(Exception e){
               e.printStackTrace();
           }
       }
   },"1",1<<26).start();
   }
    static StringBuilder sb;
    public static void test(){
         sb=new StringBuilder();
        int t=nextInt();
        while(t-->0){
            
            solve();
           
        }
        pw.println(sb);
    }
    public static long pow(long n, long p,long mod) {
        if(p==0)
            return 1;
        if(p==1)
            return n%mod;
        if(p%2==0){
            long temp=pow(n, p/2,mod);
        return (temp*temp)%mod;
        }else{
                 long temp=pow(n,p/2,mod);
                 temp=(temp*temp)%mod;
                 return(temp*n)%mod;
                 
        }
    }
    public static long pow(long n, long p) {
        if(p==0)
            return 1;
        if(p==1)
            return n;
        if(p%2==0){
            long temp=pow(n, p/2);
        return (temp*temp);
        }else{
                 long temp=pow(n,p/2);
                 temp=(temp*temp);
                 return(temp*n);
                 
        }
    }
    public static void Merge(long a[],int p,int r){
        if(p<r){
            int q = (p+r)/2;
            Merge(a,p,q);
            Merge(a,q+1,r);
            Merge_Array(a,p,q,r);
        }
    }
    public static void Merge_Array(long a[],int p,int q,int r){
       long b[] = new long[q-p+1];
        long c[] = new long[r-q];
        for(int i=0;i<b.length;i++)
            b[i] = a[p+i];
        for(int i=0;i<c.length;i++)
            c[i] = a[q+i+1];
        int i = 0,j = 0;
        for(int k=p;k<=r;k++){
            if(i==b.length){
                a[k] = c[j];
                j++;
            }
            else if(j==c.length){
                a[k] = b[i];
                i++;
            }
            else if(b[i]<c[j]){
                a[k] = b[i];
                i++;
            }
            else{
                a[k] = c[j];
                j++;
            }
        }
    }
    
  
    public static long gcd(long x, long y) {
        if (x == 0)
            return y;
        else
            return gcd( y % x,x);
    }    
    
    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;
    }
    
     //   static LinkedList<Integer> adj[];
        static ArrayList<Integer> adj[];
        static boolean Visited[];
        static HashSet<Integer> exc;
        static long oddsum[]=new long[1000001];
        static long co=0,ans=0;
        static int parent[];
        static int size[],color[],res[],k;
        static ArrayList<Integer> al[];
        static long MOD = (long)1e9 + 7;
    /*    private static void buildgraph(int n){
            adj=new LinkedList[n+1];
            Visited=new boolean[n+1];
            levl=new int[n+1];
            
            for(int i=0;i<=n;i++){
                adj[i]=new LinkedList<Integer>();
            
            }


        }
*/      
       
        static int[] levl,dist;
        static int[] eat;
      //  static int n,m;
      //  static int n;
   //     static int price[];
        //ind frog crab
   static  boolean check(char c)
    {
    	if(c!='a' && c!='e' && c!='i' && c!='o' && c!='u' )
    		return true;
    	else
    		return false;
    }
   static int nm = 1000007;
   static boolean divisor[];
   static void sprime()
   {
	   spf=new int[nm+1];
	   for(int i=2;i<nm;i++)
	   {
		   if(spf[i]!=0)
			   continue;
		   for(int j=i;j<nm;j+=i)
		   {
			   spf[j] = i;
		   }
	   }
   }
        public static void solve(){
      
        	
        	
      
      int n= nextInt();
      int k = nextInt();
      int pixel[] = new int[n];
        
        pixel = nextIntArray(n);
        
        
        int group[] = new int[256];
        Arrays.fill(group, -1);
        
        for(int i=0;i<n;i++)
        {
        	int pix = pixel[i];
        	
        	
        	if(group[pix]==-1)
        	{
        		int groupstart = Math.max(0,pix-k+1);
        		
        		if(group[groupstart]==-1)
        		{
        			for(int j=groupstart;j<=pix;j++)
        				group[j] = groupstart;
        		}
        		else if(pix - group[groupstart] +1 > k)
        		{
        			//find end of groupstart wala  group
        			int newstart = -1;
        			for(int j = groupstart;j<=pix;j++)
        			{
        				if(group[groupstart]!=group[j])
        				{
        					newstart = j;
        					break;
        				}
        			}
        			
        			if(newstart==-1)
        				group[pix] = pix;
        			else
        			{
        				for(int j=newstart;j<=pix;j++)
        					group[j] = newstart;
        				
        			}
        		}
        		else
        		{
        			for(int j=groupstart;j<=pix;j++)
        				group[j] = group[groupstart];
        		}
        	}
        }
        
        for(int i=0;i<n;i++)
        {
        	System.out.print(group[pixel[i]]+" ");
        }
        
        
        
        }
      
        static class pa implements Comparator<Integer>
    	{
    		

    		
    		public int compare(Integer a,Integer b)
    		{
    			return b-a;
    					
    		}
    	}
        static class node implements Comparable<node>
    	{
    		int u;long w;
    		
    		node(int u,long w)
    		{
    			this.u = u;
    			this.w = w; 
    		}
    		
    		public int compareTo(node other)
    		{
    			return (int)(this.w-other.w);
    					
    		}
    	}
        static long calculate(long p)
        {
        	long mod2 = 500000004;
        	p=((p%MOD)*(p+1)%MOD)%MOD;
        	p = (p * (mod2)%MOD)%MOD;
        	return p;
        }
        static String decrypt(int x)
        {
        	if(x<4)
        		return "NO";
        	ArrayList<Integer> factors = new ArrayList<>();
        	int backup = x;
        	while(x!=1)
        	{
        		int sp = spf[x];
        		factors.add(sp);
        		while(x%sp ==0)
        		x = x / sp;
        		
        	}
        	for(int i=0;i<factors.size();i++)
        	{
        		for(int j=0;j<factors.size();j++)
        		{
        			
        			if(backup % (factors.get(i)*factors.get(j)) == 0 )
        			{
        				int tt = backup / (factors.get(i)*factors.get(j));
        				
        				if(tt==1 || divisor[tt])
        					return "YES";
        					
        			}
        		}
        	}
        	return "NO";
        }
        
       static  long maxSubArraySum(int a[], int size)
        {
           long max_so_far = a[0];
           long curr_max = a[0];
         
           for (int i = 1; i < size; i++)
           {
                curr_max = Math.max(a[i], curr_max+a[i]);
                max_so_far = Math.max(max_so_far, curr_max);
           }
           return max_so_far;
        }
        
        static void seive2(int n)
        {
        	primer=new boolean[n+1];
        	Arrays.fill(primer,true);
        	primer[0]=false;
        	primer[1]=false;
        	primer[2]=true;
        	
        	for(int i=2;i*i<=n;i++)
        	{
        		if(primer[i])
        		{
        			for(int j=2*i;j<=n;j=j+i)
        			{
        				primer[j]=false;
        			}
        		}
        	}
        }
       
        
     /*   static void BITupdate(int x,int val)
        {
        	while(x<=n)
        	{
        		BIT[x]+=val;
        		x+= x & -x;
        	}
        }*/
     /*   static void update(int x,long val)
        {
      
        	val=val%MOD;
        	while(x<=n)
        	{
        		// System.out.println(x);
        	BIT[x]=(BIT[x]+val)%MOD;
        	x+=(x & -x);
        	}
        //	System.out.println("dfd");
        }*/
        static int BITsum(int x)
        		{
        	int sum=0;
        	while(x>0)
        	{
        		sum+=BIT[x];
        		x-= (x & -x);
        	}
        		return sum;
        		}
  /*      static long sum(int x)
        {
        	long sum=0;
        	while(x>0)
        	{
        		sum=(sum+BIT[x])%MOD;
        		x-=x & -x;
        	}
        	return sum;
        }*/
        static boolean union(int x,int y)
        {
        	int xr=find(x);
        	int yr=find(y);
        	if(xr==yr)
        		return false;
        	if(size[xr]<size[yr])
        	{
        		size[yr]+=size[xr];
        		parent[xr]=yr;
        	}
        	else
        	{
        		size[xr]+=size[yr];
        		parent[yr]=xr;
        		
        	}
        	return true;
        	
        }
        static int  find(int x)
        {
        	if(parent[x]==x)
        		return x;
        	else
        	{
        		parent[x]=find(parent[x]);
        		return parent[x];
        	}
        	
        }
        public static class Edge implements Comparable<Edge>
        {
        	int u, v;
			public Edge(int u, int v) 
			{
				this.u = u;
				this.v = v;
				//this.s = s;
			}
			public int hashCode() 
			{
				return Objects.hash();
			}
			public int compareTo(Edge other) 
			{
			return (Integer.compare(u, other.u) != 0 ? (Integer.compare(u, other.u)):(Integer.compare(v, other.v)));
				//		&((Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s)):(Long.compare(u, other.v)!=0?Long.compare(u, other.v):Long.compare(v, other.u))));
				//return this.u-other.u;
			}
			public String toString()
			{
				return this.u + " " + this.v;
			}
        }
       
        static int col[];
    public static boolean isVowel(char c){
        if(c=='a' || c=='e'||c=='i' || c=='o' || c=='u')
            return true;
        return false;
    }
static int no_vert=0;

  /*private static void dfs(int start){
      Visited[start]=true;
    if(al[color[start]].size()>=k)
    {
    	res[start]=al[color[start]].get(al[color[start]].size()-k);
    }
    al[color[start]].add(start);
      for(int i:adj[start]){
          if(!Visited[i])
              {
              dfs(i);
              }
      }
      (al[color[start]]).remove(al[color[start]].size()-1);
      
  }
    */
    public static String reverseString(String s) {
        StringBuilder sb = new StringBuilder(s);
        sb.reverse();
        return (sb.toString());
    }
    
  /*  
   private static void BFS(int sou){
        Queue<Integer> q=new LinkedList<Integer>();
        q.add(sou);
        Visited[sou]=true;
        levl[sou]=0;
        while(!q.isEmpty()){
            int top=q.poll();
            
            for(int i:adj[top]){
                //pw.println(i+" "+top);
            if(!Visited[i])
            {
                
                q.add(i);
                levl[i]=levl[top]+1;
            }
            
            Visited[i]=true;
            
            }
        }
    }*/
    



                  static int indeg[];
               /* private static void kahn(int n){
                    
                    PriorityQueue<Integer> q=new PriorityQueue<Integer>();
                    for(int i=1;i<=n;i++){
                        if(indeg[i]==0){
                            q.add(i);
                        }
                    }
                    while(!q.isEmpty()){
                        int top=q.poll();
                        st.push(top);
                        for(Node i:adj[top]){
                            indeg[i.to]--;
                            if(indeg[i.to]==0){
                                q.add(i.to);
                            }
                        }
                    }
                }
                    
                    static int state=1;
                    static long no_exc=0,no_vert=0;
                  static Stack<Integer> st;
                  static HashSet<Integer> inset;
                 /*   private static void topo(int curr){
                        
                        Visited[curr]=true;
                        inset.add(curr);
                        for(int x:adj[curr]){
                            if(adj[x].contains(curr) || inset.contains(x)){
                                state=0;
                                return;
                            }
                            if(state==0)
                                return;
                            
                        }
                        st.push(curr);
                        
                        inset.remove(curr);
                    }*/
                    static HashSet<Integer> hs;
                   
                 
                     static boolean prime[];
                    static int spf[];
                    public static void sieve(int n){
                        prime=new boolean[n+1];
                        spf=new int[n+1];
                        
                        Arrays.fill(spf, 1);
                        Arrays.fill(prime, true);
                    prime[1]=false;
                        spf[2]=2;
                        
                    
                    for(int i=2;i*i<=n;i++){
                        if(prime[i]){
                            spf[i]=i;
                            for(int j=2*i;j<=n;j+=i){
                                
                                prime[j]=false;
                           
                            }
                        }
                    }
                    
                        
                    }
                     
                    // To Get Input
// Some Buffer Methods
 
                     public static void sort(long a[]){
                         Merge(a, 0, a.length-1);
                     }
                    public static void InputReader(InputStream stream1) {
                        stream = stream1;
                    }
 
                    private static boolean isWhitespace(int c) {
                        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
                    }
 
                    private static boolean isEndOfLine(int c) {
                        return c == '\n' || c == '\r' || c == -1;
                    }
 
                    private static int read() {
                        if (numChars == -1)
                            throw new InputMismatchException();
                        if (curChar >= numChars) {
                            curChar = 0;
                            try {
                                numChars = stream.read(buf);
                            } catch (IOException e) {
                                throw new InputMismatchException();
                            }
                            if (numChars <= 0)
                                return -1;
                        }
                        return buf[curChar++];
                    }
 
                    private static 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;
                    }
 
                    private static 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;
                    }
 
                    private static String nextToken() {
                        int c = read();
                        while (isSpaceChar(c))
                            c = read();
                        StringBuilder res = new StringBuilder();
                        do {
                            res.appendCodePoint(c);
                            c = read();
                        } while (!isSpaceChar(c));
                        return res.toString();
                    }
 
                    private static 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();
                    }
 
                    private static int[] nextIntArray(int n) {
                        int[] arr = new int[n];
                        for (int i = 0; i < n; i++) {
                            arr[i] = nextInt();
                        }
                        return arr;
                    }
 
                    private static long[][] next2dArray(int n, int m) {
                        long[][] arr = new long[n][m];
                        for (int i = 0; i < n; i++) {
                            for (int j = 0; j < m; j++) {
                                arr[i][j] = nextLong();
                            }
                        }
                        return arr;
                    }
                    private static char[][] nextCharArray(int n,int m){
                        char [][]c=new char[n][m];
                        for(int i=0;i<n;i++){
                            String s=nextLine();
                            for(int j=0;j<s.length();j++){
                                c[i][j]=s.charAt(j);
                            }
                        }
                        return c;
                    }
 
                    private static long[] nextLongArray(int n) {
                        long[] arr = new long[n];
                        for (int i = 0; i < n; i++) {
                            arr[i] = nextLong();
                        }
                        return arr;
                    }
 
                    private static void pArray(int[] arr) {
                        for (int i = 0; i < arr.length; i++) {
                            pw.print(arr[i] + " ");
                        }
                        pw.println();
                        return;
                    }
 
                    private static void pArray(long[] arr) {
                        for (int i = 0; i < arr.length; i++) {
                            pw.print(arr[i] + " ");
                        }
                        pw.println();
                        return;
                    }
 
                    private static void pArray(boolean[] arr) {
                        for (int i = 0; i < arr.length; i++) {
                            pw.print(arr[i] + " ");
                        }
                        pw.println();
                        return;
                    }
 
                    private static boolean isSpaceChar(int c) {
                        if (filter != null)
                            return filter.isSpaceChar(c);
                        return isWhitespace(c);
                    }
 
                    private interface SpaceCharFilter {
                        public boolean isSpaceChar(int ch);
                    }
                    

}