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.*;

public class PointSeg {

	public static void main(String[] args)
	{
		
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();//num segments
		int m = scan.nextInt();//upper bound for ultrasegment
		int[][] segs = new int[n][2];
		for(int i = 0; i < n; i++)
		{
			segs[i][0] = scan.nextInt();
			segs[i][1] = scan.nextInt();
		}
		int[] possPoints = new int[m];
		for(int i = 0; i < m; i++)
		{
			possPoints[i] = i+1;
		}
		for(int i = 0; i < n; i++)
		{
			for(int j = 0; j < possPoints.length; j++)
			{
				if(possPoints[j] >= segs[i][0] && possPoints[j] <= segs[i][1])
				{
					possPoints[j] = -1;
				}
			}
		}
		int counter = 0;
		for(int i = 0; i < possPoints.length; i++)
		{
			if(possPoints[i] != -1)
			{
				counter++;
			}
		}
		if(counter > 0)
		{
			System.out.println(counter);
			for(int i = 0; i < possPoints.length; i++)
			{
				if(possPoints[i] != -1)
				{
					System.out.print(possPoints[i] + " ");
				}
			}
		}
		else
		{
			System.out.println(0);
		}
		
	}
	
}