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.BufferedWriter;
import java.io.FileWriter;
import java.io.*;
import java.util.*;
public class pointinsegment {
    
    public static void main(String [] args) throws IOException
    {
        Scanner input = new Scanner(System.in); 
   
        
        int answer =0;
        
        String str = input.nextLine();
        StringTokenizer st = new StringTokenizer(str); 
        int N = Integer.parseInt(st.nextToken()); 
        int M = Integer.parseInt(st.nextToken()); 
        boolean arr [] = new boolean [M]; 
        for(int i=0; i<arr.length; i++)
            arr[i]=false; 
        
        for(int i=0; i<N; i++)
        {
            StringTokenizer temp = new StringTokenizer(input.nextLine()); 
            int start = Integer.parseInt(temp.nextToken()); 
            int end = Integer.parseInt(temp.nextToken()); 
            for(int j=start-1; j<=end-1; j++)
                arr[j]=true;
        }
        for(int i=0; i<arr.length; i++)
        {
            if(!arr[i])
                answer++; 
       
                
        }
        int answers[] = new int [answer]; 
        int next=0; 
        for(int i=0; i<arr.length; i++)
        {
            if(!arr[i])
            {
                answers[next]=i; 
                next++; 
            }
                        
        }
        System.out.println(answer); 
        for(int i=0; i<answers.length; i++)
            System.out.print(answers[i]+1 + " ");
        
       
    }
    
    
}