Problem: You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints. 

Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.

The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.

Output

In the first line print one integer k — the number of points that don't belong to any segment.

In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.

If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.

Examples

Input

3 5
2 2
1 2
5 5


Output

2
3 4 


Input

1 7
1 7


Output

0

Note

In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.

In the second example all the points from 1 to 7 belong to the first segment.

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.Stream;

public class Practice {
	
	
	static class length implements Comparator<String>
	{
		public int compare(String a,String b)
		{
			return(a.length()-b.length());
		}
	}
	
	
	
	
	   static class FastReader
	   {
		   BufferedReader br;
		   StringTokenizer st;
		   public FastReader()
		   {
			   br = new BufferedReader(new InputStreamReader(System.in));
		   }
		   
		   
		   String next() 
	        { 
	            while (st == null || !st.hasMoreElements()) 
	            { 
	                try
	                { 
	                    st = new StringTokenizer(br.readLine()); 
	                } 
	                catch (IOException  e) 
	                { 
	                    e.printStackTrace(); 
	                } 
	            } 
	            return st.nextToken(); 
	        } 
		   
		   
		   int nextInt()
		   {
			   return Integer.parseInt(next());
		   }
		   long nextLong()
		   {
			   return Long.parseLong(next());
		   }
		   double nextDouble() 
	        { 
	            return Double.parseDouble(next()); 
	        } 
		   
		   String nextLine() 
	        { 
	            String str = ""; 
	            try
	            { 
	                str = br.readLine(); 
	            } 
	            catch (IOException e) 
	            { 
	                e.printStackTrace(); 
	            } 
	            return str; 
	        } 
	   }

		public static void main(String []args) throws Exception
		{
			//Scanner sc=new Scanner(System.in);
			FastReader in =new FastReader();
			PrintWriter pw = new PrintWriter(System.out);
			//System.out.println
			int n=in.nextInt();	
			int m=in.nextInt();	
			TreeSet<Integer> t =new TreeSet<Integer>(); 
			for(int i=0;i<n;i++)
			{
				int l=in.nextInt();
				int r=in.nextInt();
				
				for(int j=l;j<=r;j++)
				{
					t.add(j);
				}
			}
			int k=m-t.size();
			pw.println(k);
		
			Object a[]=t.toArray();
			for(int i=1;i<t.size();i++)
			{
				for(int j=(int)a[i-1]+1;j<(int)a[i];j++)
				{
					pw.print(j+" ");
				}
			}
			
			for(int i=1;i<(int)a[0];i++)
			{
				pw.print(i+" ");
			}
			for(int i=(int)a[t.size()-1]+1;i<=m;i++)
			{
				pw.print(i+" ");
			}
			
		    
					     
			
		
			
			
            pw.flush();
			pw.close();
			
	}
		
}