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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;
import java.util.StringTokenizer;

import javax.xml.parsers.DocumentBuilder;
import javax.xml.parsers.DocumentBuilderFactory;
import javax.xml.parsers.ParserConfigurationException;

import org.w3c.dom.Document;
import org.w3c.dom.NamedNodeMap;
import org.w3c.dom.Node;
import org.w3c.dom.NodeList;
import org.xml.sax.SAXException;




public class Main{
	static class MyScanner {
	    BufferedReader br;
	    StringTokenizer st;

	    public MyScanner() {
	       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 IOException, ParserConfigurationException, SAXException {
			 	PrintWriter out = new PrintWriter(System.out);
			    MyScanner sc = new MyScanner();
			 	Main solver = new Main();
				solver.solve(out, sc);
				out.flush();
				out.close();
			
		 }
	
		
		 
		 
		
 		void solve(PrintWriter out, MyScanner sc) throws IOException, ParserConfigurationException, SAXException{	
 		
 			
 				int n = sc.nextInt();
 				int m = sc.nextInt();
 				int[] a = new int[m + 2];
 				while(n-- > 0) {
 					int l = sc.nextInt();
 					int r = sc.nextInt();
 					
 					for(int i =  l ; i <= r; ++i) {
 						a[i] = 1;
 					}
 				}
 				
 				int c = 0; 
 				for(int i = 1 ; i <= m ; ++i) {
 					c += (a[i] == 0)?1:0;
 				}
 				out.println(c);
 				for(int  i = 1 ; i <= m ; ++i) {
 					if(a[i] == 0) out.print(i + " "); 
 				}
 				
 				
 		
 			
 				
		}
 	
		
		
	
			
		
		
		
		
		
		
		
		
	
	
}