There are n students standing in a row. Two coaches are forming two teams — the first coach chooses the first team and the second coach chooses the second team.

The i-th student has integer programming skill a_i. All programming skills are distinct and between 1 and n, inclusive.

Firstly, the first coach will choose the student with maximum programming skill among all students not taken into any team, and k closest students to the left of him and k closest students to the right of him (if there are less than k students to the left or to the right, all of them will be chosen). All students that are chosen leave the row and join the first team. Secondly, the second coach will make the same move (but all students chosen by him join the second team). Then again the first coach will make such move, and so on. This repeats until the row becomes empty (i. e. the process ends when each student becomes to some team).

Your problem is to determine which students will be taken into the first team and which students will be taken into the second team.

Input

The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 2 ⋅ 10^5) — the number of students and the value determining the range of chosen students during each move, respectively.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n), where a_i is the programming skill of the i-th student. It is guaranteed that all programming skills are distinct.

Output

Print a string of n characters; i-th character should be 1 if i-th student joins the first team, or 2 otherwise.

Examples

Input


5 2
2 4 5 3 1


Output


11111


Input


5 1
2 1 3 5 4


Output


22111


Input


7 1
7 2 1 3 5 4 6


Output


1121122


Input


5 1
2 4 5 3 1


Output


21112

Note

In the first example the first coach chooses the student on a position 3, and the row becomes empty (all students join the first team).

In the second example the first coach chooses the student on position 4, and the row becomes [2, 1] (students with programming skills [3, 4, 5] join the first team). Then the second coach chooses the student on position 1, and the row becomes empty (and students with programming skills [1, 2] join the second team).

In the third example the first coach chooses the student on position 1, and the row becomes [1, 3, 5, 4, 6] (students with programming skills [2, 7] join the first team). Then the second coach chooses the student on position 5, and the row becomes [1, 3, 5] (students with programming skills [4, 6] join the second team). Then the first coach chooses the student on position 3, and the row becomes [1] (students with programming skills [3, 5] join the first team). And then the second coach chooses the remaining student (and the student with programming skill 1 joins the second team).

In the fourth example the first coach chooses the student on position 3, and the row becomes [2, 1] (students with programming skills [3, 4, 5] join the first team). Then the second coach chooses the student on position 1, and the row becomes empty (and students with programming skills [1, 2] join the second team).
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.Scanner;
import java.util.TreeSet;


public class TwoTeams {
	
	/*static class Skill {
		 int index;
		 int skill;
		@Override
		public String toString() {
			return "Skill [index=" + index + ", skill=" + skill + "]";
		}
	}*/
	
	static class two implements Comparable<two>{
        int skill,index;
        two(int a, int b){
            this.skill=a;this.index=b;
        }
        @Override
        public int compareTo(two ob){
            return this.skill-ob.skill;
        }
    }


	public static void main(String[] args) {
//		Scanner s = new Scanner(System.in);
		int n = ni();
		int k = ni();
		TreeSet<Integer>  sk = new TreeSet<Integer>();
		two[] ls = new two[n];
		
		for(int i=0;i<n;i++) {
			/*Skill skill = new Skill();
			skill.index =i;
			skill.skill = s.nextInt();*/
			
			 ls[i] = new two(ni(), i);

			sk.add(i);
		}
		
		for(int i=0;i<n;i++) {
			sk.add(i);
		}
		
		int [] ar = new int[n];
		/*Comparator<two> com = new Comparator<two>() {
			
			@Override
			public int compare(two o1, two o2) {
				
				return o2.skill-o1.skill;
			}
		};*/
//		Arrays.sort(ls, com);
		Arrays.sort(ls,Collections.reverseOrder());
		
		int team =1;
		
		for(int i=0;i<n;i++) {
//			System.out.println(sl);
			two sl = ls[i];
			
			Integer index = sl.index;
			if(ar[index]==0) {
				ar[index]=team;
				sk.remove(index);
				int tempK =k;
				
				while(tempK>0) {
					Integer stemp = sk.higher(sl.index);
					if(stemp==null)
						break;
					ar[stemp] = team;
					tempK--;
					sk.remove(stemp);
				}
				
				tempK =k;
				while(tempK>0) {
					Integer stemp = sk.lower(sl.index);
					if(stemp==null)
						break;
						ar[stemp] = team;
					tempK--;
					sk.remove(stemp);
				}
				
				team++;
				if(team>2)
					team-=2;
			}
			
		}
		
//		String out = ar[0]+"";
		for(int i=0;i<n;i++) {
			System.out.print(ar[i]);
		}
		System.out.println("");
//		 for(int i=0;i<n;i++)pws(ar[i]);pl();

	}

	/*----------------------------------------------------------------------------------------------------------------*/
    //THE DON'T CARE ZONE BEGINS HERE...\\
    static int mod9 = 1000000007;
    static int n, m, l, k, t;
    static AwesomeInput input = new AwesomeInput(System.in);
    static PrintWriter pw = new PrintWriter(System.out, true);

    // The Awesome Input Code is a fast IO method //
    static class AwesomeInput {
        private InputStream letsDoIT;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        private AwesomeInput(InputStream incoming) {
            this.letsDoIT = incoming;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = letsDoIT.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        private long ForLong() {
            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 String ForString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(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;
        }

        public interface SpaceCharFilter {
            boolean isSpaceChar(int ch);
        }
    }

    // functions to take input//
    static int ni() {
        return (int) input.ForLong();
    }

    static String ns() {
        return input.ForString();
    }

    static long nl() {
        return input.ForLong();
    }

    static double nd() throws IOException {
        return Double.parseDouble(new BufferedReader(new InputStreamReader(System.in)).readLine());
    }

    //functions to give output
    static void pl() {
        pw.println();
    }

    static void p(Object o) {
        pw.print(o + " ");
    }

    static void pws(Object o) {
        pw.print(o + "");
    }

    static void pl(Object o) {
        pw.println(o);
    }

    // Fast Sort is Radix Sort
    public static int[] fastSort(int[] f) {
        int n = f.length;
        int[] to = new int[n];
        {
            int[] b = new int[65537];
            for (int i = 0; i < n; i++) b[1 + (f[i] & 0xffff)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < n; i++) to[b[f[i] & 0xffff]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        {
            int[] b = new int[65537];
            for (int i = 0; i < n; i++) b[1 + (f[i] >>> 16)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < n; i++) to[b[f[i] >>> 16]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        return f;
    }

    /*public static void main(String[] args) {      //threading has been used to increase the stack size.

        new Thread(null, null, "Vengeance", 1 << 25)  //the last parameter is stack size desired.
        {
            public void run() {
                try {
                    double s = System.currentTimeMillis();
                    MainSolution();
                    //pl(("\nExecution Time : " + ((double) System.currentTimeMillis() - s) / 1000) + " s");
                    pw.flush();
                    pw.close();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }*/
}
