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.*;
import java.util.*;

public class Solution{ 
	

	 
	
	 public static void main(String[] args) { 
	     
	     Scanner in = new Scanner(System.in);
	     
	     int n,m,k,i,j,l,r;
	     int[] c;
	     
	     n=Integer.parseInt(in.next());
	     m=Integer.parseInt(in.next());
	     
	     c=new int[m+1];
	     
	     k=0;
	     
	     for(i=1;i<=n;i++){
	    	 l=Integer.parseInt(in.next());
	    	 r=Integer.parseInt(in.next());
	    	 for(j=l;j<=r;j++) c[j]=1;
	     }
	     
	     for(i=1;i<=m;i++){
	    	 if(c[i]==0)k++;
	     }
	     
	     System.out.println(k);
	     
	     for(i=1;i<=m;i++){
	    	 if(c[i]==0){
	    		 System.out.print(i+" ");
	    	 }
	     }
	     
	     
	     
	     
	     
	 }
}