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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.sql.Array;
import java.sql.ResultSet;
import java.sql.SQLException;
import java.util.*;
import java.util.List.*;
import java.util.concurrent.Executor;
import java.util.concurrent.ExecutorService;
import java.util.concurrent.Executors;
import java.util.stream.Collector;
import java.util.stream.Collectors;

/*import org.springframework.beans.factory.xml.XmlBeanFactory;
import org.springframework.context.ApplicationContext;
import org.springframework.context.support.ClassPathXmlApplicationContext;
import org.springframework.core.io.*;
*/
public class Test {
	
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		// ApplicationContext con = new
		// ClassPathXmlApplicationContext("bean.xml");
		FastReader in = new FastReader();
		StringBuilder out = new StringBuilder();
		int n = in.nextInt();
		
		int m = in.nextInt();
		
		Set<Integer> set = new HashSet<>();
		int c =0;
		while(n-->0){
			int l = in.nextInt();
			int r = in.nextInt();

				for (int i = l; i <=r; i++) {
					set.add(i);
				}

		}
		for (int i = 1; i <= m; i++) {
		 if(!set.contains(i)){
			out.append(i+" ");
		    ++c;
		 }
		}
		if(out.toString().isEmpty()){
			System.out.println(0);
		}else{
			System.out.println(c+"\n"+out);
		}
		
}
	
	
}
class FastReader {

	BufferedReader br;
	StringTokenizer st;

	public FastReader() {
		br = new BufferedReader(new InputStreamReader(System.in));

	}

	public String next() {
		while (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(br.readLine());

			} catch (IOException e) {
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public long nextLong() {
		return Long.parseLong(next());
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}

	public String nextLine() {
		String str = "";
		try {
			str = br.readLine();
		} catch (IOException e) {
			e.printStackTrace();
		}
		return str;
	}
}