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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.BufferedReader;
import java.util.LinkedList;
import java.util.Locale;
import java.util.Iterator;
import java.util.Stack;
import java.util.TreeSet;
import java.util.Set;
import java.util.HashSet;
import java.util.HashMap;
import java.util.Map;
public class UvaProblems {
			
	public static void main(String[] args) throws Exception{
			
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		Locale.setDefault(new Locale("en", "US"));

		String[] a =  in.readLine().split(" ");
		String[] b ;
		int cont = 0;
		ArrayList<Integer> sec = new ArrayList<>();
		ArrayList<Integer> sec1 = new ArrayList<>();
		for(int i  =0; i<Integer.parseInt(a[0]); i++) {
			b = in.readLine().split(" ");
			for(int j = Integer.parseInt(b[0]); j<=Integer.parseInt(b[1]); j++) {
				if(!sec.contains(j))
					sec.add(j);
			}
		}
		for(int k = 1; k<= Integer.parseInt(a[1]); k++) {
			if(!sec.contains(k)) {
				cont++;
				sec1.add(k);
			}
		}
		out.println(cont);
		if(sec.isEmpty())
			out.println("");
		else {
			for(int num : sec1)
				out.print(num + " ");
		}
		
		
		
		
		
		
		
		out.flush();
	}

}