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.util.*;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;
import java.lang.*;
import java.io.*;

public class chinu
{
	public static void main (String[] args)
	{
		Scanner s = new Scanner(System.in);
	    
            int n = s.nextInt();
            int max = s.nextInt();
            
            Set<Integer> v = new HashSet<Integer>();
            int[] l = new int[n];
            int[] r = new int[n];
            
            Vector<Integer> f = new Vector<Integer>(); 

            for(int i = 0; i < n; i++){
                l[i] = s.nextInt();
                r[i] = s.nextInt();
            }
            
            for(int i = 0; i < n; i++){
                for(int j = l[i]; j <= r[i]; j++){
                    v.add(j);
                }
            }

            for(int i = 1; i <= max; i++){
                if(v.contains(i))
                    continue;
                else
                    f.add(i);
            }

            
            
            if(f.size() == 0){
                System.out.print(0);
            } else {
                System.out.println(f.size());
                Iterator itr = f.iterator();
                while(itr.hasNext()){
                System.out.print(itr.next()+" ");
                }
            }

		    
		
	}
}