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.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class Test {
	
	    public static void main(String[] args) {
	    	 	  Scanner br=new Scanner(System.in);
		         int numberOfSeg=br.nextInt();
		         int MaxElem=br.nextInt();
		         int l,r,monPoint;
		        
		       List<Integer> maListe=new ArrayList<Integer>();
		        int[] elem=new int[MaxElem+1];
		        
		        for(int i=1;i<=numberOfSeg;i++) {
		        	l=br.nextInt();
		        	r=br.nextInt();
		        	for(int j=l;j<=r;j++) {
		        		elem[j] = 1;
		        	}
		        }
		        
		        for (int i = 1; i < MaxElem+1; i++) {
		        	monPoint = elem[i];
		            if (monPoint==0)   maListe.add(i);		        
		        }

		        StringBuilder res = new StringBuilder(maListe.size() + "\n");
		        String resultas=maListe.size() + "\n";
		        for (Integer point : maListe) {
		            res.append(point).append(" ");
		            resultas+=point+" ";
		        }

		        System.out.println(resultas);
	    }
}