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:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */


import java.util.ArrayList;
import java.util.Scanner;

/**
 *
 * @author A07025360
 */
public class APointsInSegments {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        ArrayList a = new ArrayList();
        ArrayList e = new ArrayList();
        ArrayList g = new ArrayList();
        int n = scan.nextInt();
        int m = scan.nextInt();
        int count = m;
        
        for (int i = 1; i <= m; i++){
            a.add(i);
            }
        
        for (int i = 0; i < n; i++){
            int b = scan.nextInt();
            int c = scan.nextInt();
            int x = c-b;
            if (x==0){
                e.add(c);
            } else {
                for (int y = b;y<=c;y++){
                    e.add(y);
                }
            }
            }
        
        for (int i = 0; i < m; i++){
            for (int f = 0; f < e.size(); f++){
            if (a.get(i)==e.get(f)){
                a.set(i, 0);
                count--;
            } 
            }
            }
        System.out.println(count);
        for (int i = 0; i < m; i++){
            if ((int)a.get(i)!=0){
                g.add(a.get(i));
            }
            }
        String t = String.join("", g.toString());
        System.out.println(t.replace("[","").replaceAll(",","").replace("]", ""));
        }
        
    }