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:

/**
 *
 * @author Daipayan Mukherjee
 */

import java.io.*;
import java.util.*;


public class codeforces31stJuly_1 {

public static void main(String args[])throws IOException{
    
    BufferedReader br= new BufferedReader(new InputStreamReader(System.in));
    
    String s=br.readLine();
    String st[]=s.split(" ");
    
    int n=Integer.parseInt(st[0]);
    int m=Integer.parseInt(st[1]);
    
    int start[]=new int[n];
    int end[]=new int[n];
    
    for(int i=1;i<=n;i++){
           String sq=br.readLine();
           String sy[]=sq.split(" ");
           start[i-1]=Integer.parseInt(sy[0]);
           end[i-1]=Integer.parseInt(sy[1]);
    }
    
    int count=0;
    int flag=0;
    int arr[]=new int[m];
    int k=-1;
    Arrays.fill(arr,0);
    
    for(int i=1;i<=m;i++){
        
        flag=0;
        
        for(int j=0;j<n;j++){
            if(i>=start[j]&&i<=end[j])
                flag=1;
        }
        if(flag==0){
            ++count;
            arr[++k]=i;
        }
        
    }
    System.out.println(count);
    
    for(int i=0;i<arr.length;i++){
        if(arr[i]!=0)
            System.out.print(arr[i]+" ");
    }

    
    
    
}

    
}