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.*;

public class pro
{
    
    
    public static boolean vowel(char c){
        if(c=='A'||c=='E'||c=='I'||c=='O'||c=='U'||c=='a'||c=='e'||c=='i'||c=='o'||c=='u')
        return true;
        return false;
    }
    
    public static boolean check(long a)
    {
        while(a%2==0)
            a/=2;
        while(a%3==0)
            a/=3;
        if(a!=1)
            return false;
        return true;
    }
    public static void main(String args[])
    {
      Scanner sc = new Scanner(System.in);
      int l =sc.nextInt();
      int b =sc.nextInt();
      int x1[] = new int[l];
      int x2[] = new int[l];
      List<Integer> a = new ArrayList<Integer>();
      for(int i=0;i<l;i++)
      {
        x1[i] = sc.nextInt();
        x2[i] = sc.nextInt();
      }
      for(int i=1;i<=b;i++)
      {
          a.add(i);
      }
      for(int i=0;i<l;i++)
      {
          for(int k = x1[i];k<=x2[i];k++)
          {
              if(a.indexOf(k)!=-1)
              {
                  a.remove(a.indexOf(k));
              }
          }
      }
      if(a.size()>=1)
      {
        System.out.println(a.size());
        for(int i=0;i<a.size();i++)
            System.out.print(a.get(i)+" ");
      }
      else
        System.out.println(0);
    }
}