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.File;
import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;
public class A1015 
{
    public static void main(String[] args) throws FileNotFoundException{
    	 
        Scanner scan = new Scanner(System.in);
        int coordinates = scan.nextInt();
        int upper = scan.nextInt();
        ArrayList<Integer> first = new ArrayList<Integer>();
        ArrayList<Integer> second = new ArrayList<Integer>();
        ArrayList<Integer> ooga = new ArrayList<Integer>();
        int bint = 0;
        while(scan.hasNextInt()) {
        	int temp = scan.nextInt();
        	if(bint % 2 == 0) {
        		first.add(temp);
        	}else {
        		second.add(temp);
        	}
        	bint++;
        }
      //  System.out.println(first);
     //   System.out.println(second);
        for(int i =0 ; i < coordinates; i ++) {
        	//if(first.get(i) != second.get(i)) {
        		for(int j = first.get(i); j <= second.get(i); j ++) {
        			//System.out.println(first.get(i) + " " + second.get(i));
        			if(!ooga.contains(j))
        			ooga.add(j);
        		}
        	/*}else {
        		ooga.add(first.get(i));
        	}
        	*/
        }
        Collections.sort(ooga);
       // System.out.println(ooga);
        
        System.out.println(upper - ooga.size() );
        for(int i = 1 ; i <= upper; i ++) {
        	if(!ooga.contains(i) && i != upper) {
        		System.out.print(i + " ");
        	}else if(!ooga.contains(i)) { 		
        		System.out.print(i);
        	}
        	
        }

    }
}