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.*;
import java.lang.*;
import java.io.*;
public class PointsInSegments{
	public static void main(String args[])throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
		String str[] = br.readLine().trim().split("\\s+");
		int q = Integer.parseInt(str[0]);
		int num = Integer.parseInt(str[1]);
		HashSet<Integer> hs = new HashSet<Integer>();
		while(q-->0){
			String arr[] = br.readLine().trim().split("\\s+");
			int val1 = Integer.parseInt(arr[0]);
			int val2 = Integer.parseInt(arr[1]);
			for(int i=val1;i<=val2;i++){
				hs.add(i);
			}
		}
		int count = num-hs.size();
		bw.write(count+"\n");
		for(int i=1;i<=num;i++){
			if(!hs.contains(i))
			bw.write(i+" ");
		}
		bw.write("\n");
		bw.close();
	}
}