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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;


public class PointsInSegments {
     public static void fullArr(ArrayList<Integer>list, int m){
           for (int i = 1; i <= m; i++) {
                  list.add(i);
         }
     }
    public static void main(String[] args) throws IOException {
      BufferedReader  in = new BufferedReader(new InputStreamReader(System.in));
       
        StringTokenizer tk1  = new StringTokenizer(in.readLine());
        int n, m, l, r;
         n = Integer.parseInt(tk1.nextToken());
         m = Integer.parseInt(tk1.nextToken());
        
         ArrayList<Integer> list = new ArrayList();
         ArrayList<Integer> temp = new ArrayList();
          ArrayList<Integer> res = new ArrayList();
         
         fullArr(list, m);
         
         for (int i = 0; i < n; i++) {
           StringTokenizer tk2 = new StringTokenizer(in.readLine());
           l = Integer.parseInt(tk2.nextToken());
           r = Integer.parseInt(tk2.nextToken());
   
             for (int j = l; j <= r; j++) {
                 if(! temp.contains(j)){
                      temp.add(j);
                 }
             }
        }
         for (int i = 0; i < list.size(); i++) {
             int te = list.get(i);
             if(!temp.contains(te)){
                 res.add(te);
             }
        }
        
         System.out.println(res.size());
         for (int i = 0; i < res.size(); i++) {
             System.out.print(res.get(i)+" ");
        }
        
    }
    
}