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.Scanner;
import java.io.*;
import java.util.ArrayList;
import java.util.List;
public class MyClass {
    public static void main(String args[]) {
      Scanner sc = new Scanner(System.in);

      int lines = sc.nextInt();
      int upper = sc.nextInt();
      sc.nextLine();
      
      int[][] segments = new int[lines][2];
      
      List<Integer> dontBelong = new ArrayList<Integer>();
      
      for(int i = 0; i < lines; i++){
          segments[i][0] = sc.nextInt();
          segments[i][1] = sc.nextInt();
          sc.nextLine();
      }
      
      for(int n = 1; n <= upper; n++){
          boolean belongs = false;
          //System.out.println(n + " " + belongs);
          for(int i = 0; i < lines; i++){
              if(n >= segments[i][0] && n <= segments[i][1]){
                  //System.out.println("entrei");
                  belongs = true;
                  //break;
              }
              //System.out.println(n + " " + segments[i][0] + " " + segments[i][1] + " " + belongs);
          }
          
          if(!belongs) dontBelong.add(n);
      }
      
      System.out.println(dontBelong.size());
      for(int i = 0; i < dontBelong.size(); i++){
          System.out.print(dontBelong.get(i) + " ");
      }
    }
}