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;
import java.util.Collections;
import java.util.HashSet;
import java.util.LinkedList;
import java.awt.List;
import java.util.ArrayList;

public class Solution {

    @SuppressWarnings("resource")
	public static void main(String[] args){
    	
    	Scanner input = new Scanner(System.in);
    	
    	int n = input.nextInt(), m = input.nextInt();
    	int[][] points = new int[n][2];
    	int counter = 0;
    	LinkedList<Integer> points2 = new LinkedList<Integer>();
    	
        for(int i = 0; i < n; i++) {
        	points[i][0] = input.nextInt();
        	points[i][1] = input.nextInt();        	
        }
        
        for(int i = 1; i <= m; i++) {
        	int counterPoints = 0;
        	for(int j = 0; j < n; j++) {
        		if(i < points[j][0] || i > points[j][1])
        			counterPoints++;
        	}
        	
        	if(counterPoints >= n) {
        		counter++;
        		points2.add(i);
        	}	
        }
        
        System.out.println(counter);
        
        for(int i : points2)
        	System.out.print(i + " ");   		
    }    
}