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.IOException;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Scanner;

public class codeforces {

	public static void main(String[] args)throws IOException 
	{
	  Scanner in = new Scanner(System.in);	
	  int n=in.nextInt();
	  int m= in.nextInt();
	  int i=0,j=0,k=0;
	 HashSet<Integer> hs = new HashSet<Integer>();
	 for(i=0;i<n;i++)
	 {
		 int a=in.nextInt();
		 int b=in.nextInt();
		 for(j=a;j<=b;j++)
		 {
			 hs.add(j);
		 }
	 }
	 
	 ArrayList<Integer> lt = new ArrayList<Integer>();
	 for(i=1;i<=m;i++)
	 {
		 if(hs.contains(i)==false)
		 {
			 k++;
			 lt.add(i);
		 }
	 }
	  
	 if(k==0)
	 {
		 System.out.println(k);
	 }
	 else
	 {
		 System.out.println(k);
		 
		 for(i=0;i<lt.size();i++)
		 {
			 System.out.print(lt.get(i)+" ");
		 }
	 }
	  
    }
		
	}