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.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Main
{
	static PrintStream out = System.out;
	static PrintStream err = System.err;
	static final int INF = 1000000000;
	
	public static void main(String[] args)
	{
		Scanner in = new Scanner(System.in);
		// if necessary
		// BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		// PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		int n = in.nextInt();
		int m = in.nextInt();
		BitSet bs = new BitSet(m);
		for (int i = 0; i < n; ++i) {
			int l = in.nextInt() - 1, r = in.nextInt();
			bs.set(l, r);
		}
		out.println(m - bs.cardinality());
		// out.println(bs.toString());
		for (int i = 0; i < m; ++i) {
			if (!bs.get(i))
				out.print((i + 1) + " ");
		}
		out.println();
		
		// pr.close();
	}
}