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 Prog1015A2{
   public static void main(String[] args){
      Scanner sc=new Scanner(System.in);
      byte n=sc.nextByte();
      byte m=sc.nextByte();
      byte[] start=new byte[n];
      byte[] end=new byte[n];
      for(byte i=0;i<n;i++){
         start[i]=sc.nextByte();
         end[i]=sc.nextByte();
      }
      byte i=1;
      boolean present=false;
      ArrayList<Byte> points=new ArrayList<Byte>();
      while(i<=m){
         present=false;
         for (byte j=0;j<n;j++){
            if(i>=start[j]&&i<=end[j]){
               present=true;
            }
         }
         if(present==false){
            points.add(i);
         }
         i++;
      }
      System.out.println(points.size());
      for (byte q:points){
         System.out.print(q+" ");
      }
   }
}