Problem: User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:

<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>

When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.

There are some conditions in the navigation:

  * If page 1 is in the navigation, the button "<<" must not be printed. 
  * If page n is in the navigation, the button ">>" must not be printed. 
  * If the page number is smaller than 1 or greater than n, it must not be printed. 



You can see some examples of the navigations. Make a program that prints the navigation.

Input

The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)

Output

Print the proper navigation. Follow the format of the output from the test samples.

Examples

Input

17 5 2


Output

&lt;&lt; 3 4 (5) 6 7 &gt;&gt; 

Input

6 5 2


Output

&lt;&lt; 3 4 (5) 6 

Input

6 1 2


Output

(1) 2 3 &gt;&gt; 

Input

6 2 2


Output

1 (2) 3 4 &gt;&gt;

Input

9 6 3


Output

&lt;&lt; 3 4 5 (6) 7 8 9

Input

10 6 3


Output

&lt;&lt; 3 4 5 (6) 7 8 9 &gt;&gt;

Input

8 5 4


Output

1 2 3 4 (5) 6 7 8 

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        FasterScanner s = new FasterScanner();
        PrintWriter out=new PrintWriter(System.out);
        
        
        
        int n=s.nextInt();
        int p=s.nextInt();
        int k=s.nextInt();
        
        if(1<p-k)
        	System.out.print("<< ");
        for(int i=p-k;i<=p+k;i++)
        {
        	if(i>=1 && i<=n)
        	{
        		if(i==p)
        			System.out.print("("+i+") ");
        		else 
        		System.out.print(i+" ");
        	}
        }
        if(p+k<n)
        	System.out.println(">>");
        
        
        
        
    }
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    static class Node implements Comparable<Node>
    {
    	long w;
    	int id;
    	int c;
    	Node(long w2,int id2,int c2)
    	{
    		w=w2;
    		id=id2;
    		c=c2;
    	}
		@Override
		public int compareTo(Node o) {
			if(o.w!=w)
				return -Long.compare(o.w,w);
			return Long.compare(id, o.id);
		}
    }
    static int gcd (long m, long n){
        long x;
        long y;
        while(m%n != 0){
            x = n;
            y = m%n;
            m = x;
            n = y;
        }
        return (int) n;
    }

    
	public static class st {
	
	    static int n;
	    static int[] t;
	    static int [] pos;
	   
	    static void build(int n2,int[] b) {  // build the tree
	       t=b;
	       n=n2;
	       pos=new int[2*n];
	       for(int i=n;i<2*n;i++)
	       {
	    	   pos[i]=i-n;
	       }
	        for (int i = n - 1; i > 0; --i)
	        {
	        	if(t[pos[i<<1]]>t[pos[i<<1|1]])
	        		pos[i]=pos[i<<1];
	        	else
	        		pos[i]=pos[i<<1|1];
	        }
	    }
	
	    static void modify(int p, int value) {  // set value at position p
	      for (t[p += n] = value; p > 1; p >>= 1) t[p>>1] = Math.max(t[p] , t[p^1]);
	    }
	
	    static int query(int l, int r) {  // sum on interval [l, r)
	      long res=-1;
	      int p=0;
	      for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
	            if ((l&1)!=0) {
	            	if(res<t[pos[l]])
	            	{
	            		res=t[pos[l]];
	            		p=pos[l];
	            	}
	            	l++;
	            }
	            if ((r&1)!=0){
	            	r--;
	            	if(res<t[pos[r]])
	            	{
	            		res=t[pos[r]];
	            		p=pos[r];
	            	}
	            }
	          }
	      return p;
	    }
	}
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    public static class FasterScanner {
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

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

        public 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();
        }

        public String nextString() {
            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 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;
        }

        public 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;
        }
          
        public int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }
      
        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }
}