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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;


public class Main {

	public static void main(String[] args) throws IOException, InterruptedException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskC {
		static boolean visited[]  ;
		static boolean found = false; 

		static int steps = 0 ;
		static int n ; 
		static boolean memo [][] ; 
		static int dp[][] ; 
		static char matrix[][] ;
		static ArrayList<Integer> p  ;
		public void solve(int testNumber, InputReader in, PrintWriter out) throws IOException, InterruptedException {
			//			int n =  in.nextInt() ; 
			//			int a[] = new int[n] ; 
			//
			//			HashMap<Integer, Integer> x = new HashMap<Integer , Integer>() ; 
			//
			//			// 1: this sequence can't contain dupplicates
			//          //2: for every number x belong to the sequence 
			//               only 2x or x/3 will be in the sequence 
			//               cann't be both
			//			Vertix[] g = new Vertix[n] ; 
			//
			//			for (int i = 0; i < a.length; i++)
			//			{
			//				a[i]=in.nextInt() ; 
			//				x.put(a[i], i) ;
			//				g[i]= new Vertix(a[i]) ; 
			//			}
			//			int x1,x2 =0 ;
			//			for (int i = 0; i < n; i++)
			//			{
			//				if(a[i]%3==0)
			//				{
			//					x2 = a[i]/3 ; 
			//				}
			//				x1 = 2*a[i] ; 
			//				if(x.containsKey(x1))
			//					
			//
			//			}
			//

			int n = in.nextInt() ; 
			int k = in.nextInt() ; 

			int a[] = new int[n] ; 
			for (int i = 0; i < a.length; i++)
			{
				a[i] = in.nextInt() ;
			}

			int col[]= new int[256];
			int coll [] = new int[256] ; 
			for (int i = 0; i < coll.length; i++)
			{
				coll[i]=-1 ;
			}
			Arrays.fill(col, -1);


			int b[]= new int[n] ;
			//			b[0]= Math.max(0 ,a[0]-k+1) ; 
			//			
			//			
			//			for (int j = b[0]; j <  b[0]+k; j++)
			//			{
			//				if(j<256)col[j]=b[0] ;
			//			}



			for (int i = 0; i < n; i++)
			{
				if(col[a[i]]==-1)
				{

					for (int j = a[i]-k+1; j <= a[i]; j++)
					{
						if(j>=0 && j<256)
						{if(col[j]==-1 || coll[j]>=a[i])
						{
							col[a[i]]=j ;
							b[i]=j ; 
							break ;
						}
						}
					}
					for (int j = b[i]; j <= a[i]; j++)
					{
						col[j]=b[i] ;
					}


					for (int j = b[i]; j <= a[i]; j++)
					{
						coll[j]=b[i]+(k-1) ;
					}



					//					for (int j = b[i]; j <  b[i]+k; j++)
					//					{
					//						if(j<256)col[j]=b[i] ;
					//					}

					//					for (int j = a[i]; j > a[0]-k; j--)
					//					{
					//						if(j>=0) col[j]=b[i] ;
					//					}

				} else 
				{
					b[i] = col[a[i]] ;
				}

			}


			for (int i = 0; i < n; i++)
			{
				System.out.print(b[i]+" ");
			}














		}

		public static int cnt1(int mat[][])  //how many swaps to be a 1 matrix
		{
			int m = mat.length ; 
			int c=0 ; 
			for (int i = 0; i < mat.length; i++)
			{
				for (int j = 0; j < mat.length; j++)
				{
					int x =  (i*m) +j ;
					if(x%2==0 && mat[i][j]==0)
						c++; 
					if(x%2!=0 && mat[i][j]==1)
						c++; 

				}
			}
			return c;
		}
		public static int cnt0(int mat[][])
		{
			int m = mat.length ; 
			int c=0 ; 
			for (int i = 0; i < mat.length; i++)
			{
				for (int j = 0; j < mat.length; j++)
				{
					int x =  (i*m) +j ; 
					if(x%2!=0 && mat[i][j]==0)
						c++; 
					if(x%2==0 && mat[i][j]==1)
						c++; 

				}
			}
			return c;
		}

		public static boolean canFit2(int x1, int y1 , int x2 , int y2 , int x3 , int y3){
			if(x1==x2)
				if(x1==x3)
					return true ; 
				else
					return false ;
			else
				if(x1==x3)
					return false ; 
				else
				{
					long a = 1l*(y2-y1)*(x3-x2) ; 
					long b = 1l*(y3-y2)*(x2-x1) ; 

					if(a==b)
						return true;
					else 
						return false ;

				}

		}
		public static void shuffle(int c[]){
			if(c.length==1)
				return ; 
			for (int i = 0; i < c.length; i++)
			{
				Random rand = new Random();

				int  n = rand.nextInt(c.length-1) + 0;

				int temp = c[i] ; 
				c[i] = c[n] ; 
				c[n] = temp ;
			}
		}
		public static int binary(ArrayList<Long> arr, int l, int r, long x)   /// begin by 0 and n-1
		{
			if (r>=l)
			{
				int mid = l + (r - l)/2;
				if (arr.get(mid) == x)
					return mid;
				if (arr.get(mid)> x)
					return binary(arr, l, mid-1, x);
				return binary(arr, mid+1, r, x);
			}
			return -1;
		}

		/// searching for the index of first elment greater than x
		public static int binary1(ArrayList<Long> arr , long left) {
			int low = 0, high = arr.size(); // numElems is the size of the array i.e arr.size() 
			while (low != high) {
				int mid = (low + high) / 2; // Or a fancy way to avoid int overflow
				if (arr.get(mid) <= left) {
					/* This index, and everything below it, must not be the first element
					 * greater than what we're looking for because this element is no greater
					 * than the element.
					 */
					low = mid + 1;
				}
				else {
					/* This element is at least as large as the element, so anything after it can't
					 * be the first element that's at least as large.
					 */
					high = mid;
				}
			}
			return low ; // return high ; 
		}


		private static boolean triangle(int a, int b , int c){
			if(a+b>c && a+c>b && b+c>a)
				return true ; 
			else 
				return false ;
		}
		private static boolean segment(int a, int b , int c){
			if(a+b==c || a+c==b && b+c==a)
				return true ; 
			else 
				return false ;
		}
		private static int gcdThing(long a, long b) {
			BigInteger b1 = BigInteger.valueOf(a);
			BigInteger b2 = BigInteger.valueOf(b);
			BigInteger gcd = b1.gcd(b2);
			return gcd.intValue();
		}

		public static boolean is(int i){
			if(Math.log(i)/ Math.log(2) ==(int) (Math.log(i)/ Math.log(2)))
				return true ; 
			if(Math.log(i)/ Math.log(3) ==(int) (Math.log(i)/ Math.log(3)) )
				return true ; 
			if(Math.log(i)/ Math.log(6) ==(int) (Math.log(i)/ Math.log(6)) )
				return true ; 

			return false;

		}
		public static boolean contains(int b[] , int x)
		{
			for (int i = 0; i < b.length; i++)
			{
				if(b[i]==x)
					return true ;
			}
			return false ;
		}
		public static int binary(long []arr , long target , int low , long shift) {
			int high = arr.length; 
			while (low != high) {
				int mid = (low + high) / 2; 
				if (arr[mid]-shift <= target) {
					low = mid + 1;
				}
				else {
					high = mid;
				}
			}
			return low ; // return high ; 
		}
		public static boolean isLetter(char x){
			if(x+0 <=122 && x+0 >=97 )
				return true ;
			else if (x+0 <=90 && x+0 >=65 )
				return true ; 
			else return false; 
		}
		public static long getPrimes(long x ){
			if(x==2 || x==3 || x==1)
				return 2 ;
			if(isPrime(x))
				return 5 ;
			for (int i = 2; i*i<=x; i++)
			{
				if(x%i==0 && isPrime(i))
					return getPrimes(x/i) ;
			}
			return -1;
		}
		public static String solve(String x){

			int n = x.length() ; 
			String y = "" ;
			for (int i = 0; i < n-2; i+=2)
			{
				if(ifPalindrome(x.substring(i, i+2)))
					y+= x.substring(i, i+2) ;
				else 
					break ;
			}
			return y+ solve1(x.substring(y.length(),x.length())) ;

		}
		public static String solve1(String x){
			String y = x.substring(0 , x.length()/2) ; 
			return "" ;

		}
		public static String reverse(String x){
			String y ="" ;
			for (int i = 0; i < x.length(); i++)
			{
				y  = x.charAt(i) + y ;
			}
			return y ;
		}

		public static boolean ifPalindrome(String x){
			int numbers[] = new int[10] ; 
			for (int i = 0; i < x.length(); i++)
			{
				int z = Integer.parseInt(x.charAt(i)+"") ; 
				numbers[z] ++ ;
			}
			for (int i = 0; i < numbers.length; i++)
			{
				if(numbers[i]%2!=0)
					return false; 
			}
			return true ;	
		}

		public static int get(int n){
			return n*(n+1)/2 ; 
		}
		//		public static long getSmallestDivisor( long y){
		//			if(isPrime(y))
		//				return -1;
		//
		//			for (long i = 2; i*i <= y; i++)
		//			{
		//				if(y%i ==0)
		//				{
		//					return i;
		//				}
		//			}
		//			return -1;
		//		}
		//		public static void lis(pair []a , int n){
		//			int lis[] = new int[n] ; 
		//			Arrays.fill(lis,1) ; 
		//
		//			for(int i=1;i<n;i++)
		//				for(int j=0 ; j<i; j++)
		//					if (a[i].y>a[j].y &&  lis[i] < lis[j]+1)   
		//						lis[i] = lis[j] + 1;           
		//
		//			int max = lis[0];
		//
		//			for(int i=1; i<n ; i++)
		//				if (max < lis[i])
		//					max = lis[i] ;
		//			System.out.println(max);
		//
		//			ArrayList<Integer> s = new ArrayList<Integer>() ;
		//			for (int i = n-1; i >=0; i--)
		//			{
		//				if(lis[i]==max)
		//				{
		//					s.add(a[i].z);
		//					max --; 
		//				}
		//			}
		//
		//			for (int i = s.size()-1 ; i>=0 ;  i--)
		//			{
		//				System.out.print(s.get(i)+" ");
		//			}
		//
		//			return  ; 
		//		}
		public static int calcDepth(Vertix node){
			if(node.depth>0) return node.depth; 
			// meaning it has been updated before;
			if(node.parent != null)
				return 1+ calcDepth(node.parent);
			else
				return -1;
		}

		public static boolean isPrime (long num){
			if (num < 2) return false;
			if (num == 2) return true;
			if (num % 2 == 0) return false;
			for (int i = 3; i * i <= num; i += 2)
				if (num % i == 0) return false;
			return true;
		}


		public static int[] getDiv(int n)
		{
			int result[] = new int[7] ; 
			ArrayList<Integer>  f = new ArrayList<Integer>() ; 

			while (n%2==0)
			{
				if(!f.contains(2))f.add(2) ;
				n /= 2;
			}

			// n must be odd at this point.  So we can
			// skip one element (Note i = i +2)
			for (int i = 3; i <= Math.sqrt(n); i+= 2)
			{
				// While i divides n, print i and divide n
				while (n%i == 0)
				{
					if(!f.contains(i))f.add(i);
					n /= i;
				}
			}

			// This condition is to handle the case whien
			// n is a prime number greater than 2
			if (n > 2)
				if(!f.contains(n))f.add(n);

			for (int i = 0, j=0; i < f.size(); i++)
			{
				result[j++]=f.get(i);
			}
			return result ;



		}

		public static boolean dfs(Vertix v , int target){
			try{
				visited[v.i]= true ;
			} catch (NullPointerException e)
			{
				System.out.println(v.i);
			}
			if(v.i == target)

				return true ;
			for (int i =0 ; i< v.neighbours.size() ; i++)
			{ 

				Vertix child = v.neighbours.get(i) ;
				if(child.i == target){
					found = true  ; 
				}
				if(visited[child.i]==false){
					found |= dfs(child, target) ;
				}
			}
			return found; 
		}






	}
	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

	}
	public static class Vertix{
		int i ; 
		int depth ;
		ArrayList<Vertix> neighbours ; 
		Vertix parent ; 
		Vertix child ; 


		public Vertix(int i){
			this.i = i ;
			this.neighbours = new ArrayList<Vertix> () ;
			this.parent = null ;
			depth =-1;
			this.child = null ;
		}
	}

	public static class pair implements Comparable<pair>{
		int x ;  
		int y ;  




		public pair(int x, int y , int z){
			this.x=x ; 
			this.y=y ;


		}

		@Override
		public int compareTo(pair p) {
			if(this.x > p.x)
				return 1 ; 
			else return -1 ;


		}


	}


}