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.*;
import java.util.*;

public class CF_pointsinsegments {
  public static void main (String [] args) throws IOException {
    PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
    Scanner sc = new Scanner(System.in);//new File("input.txt"));

    int n = sc.nextInt();
    int m = sc.nextInt();

    HashSet<Integer> x = new HashSet<>();

    for(int i = 1; i <= m; i++){
        x.add(i);
    }

    for(int i = 0; i < n; i++){
        int a = sc.nextInt();
        int b = sc.nextInt();

        for(int j = a; j <= b; j++){
            x.remove(j);
        }
    }

    System.out.println(x.size());
    String retval = "";
    for(Integer i : x){
        retval += i+" ";
    }
    System.out.println(retval);

    out.print(x.size());
    out.println(retval);                           // output result
    out.close();                                  // close the output file
    sc.close();
  }
  
}