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.Scanner;
import java.util.Arrays;

public class SampleA501
{

	public static void main(String[] args)
	{	Scanner s = new Scanner(System.in);
                int n = s.nextInt();
                int m = s.nextInt();
                int[] a = new int[n];
                int[] b = new int[n];
                int[] d = new int[m];
                int[] c = new int[100];
                int i=0,sum=0,j=0;
                float sum1=0;
                for(i=0;i<n;i++){
                   a[i] = s.nextInt();
                   b[i] = s.nextInt();
                   
                }
                for(i=0;i<m;i++){
                   d[i] = i+1;
                }
                for(i=0;i<m;i++){
                     for(j=0;j<n;j++){
                           if(a[j]<=d[i] && d[i]<=b[j]){
                              d[i]=0;
                           } 
                     }
                }
                j=0;
                for(i=0;i<m;i++){
                     if(d[i]!=0){
                         
                         c[j]=d[i];
                         j++;
                     }
                }
                System.out.println(j);
                for(i=0;i<j;i++){
                System.out.print(c[i]+" ");
                }
                
	}
}