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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.LinkedList;
import java.util.StringTokenizer;

public class PointsInSegments {

	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter out= new BufferedWriter(new OutputStreamWriter(System.out));
		
		StringTokenizer skt=new StringTokenizer(in.readLine().trim());
		int numSeg=Integer.parseInt(skt.nextToken());
		int upperBound=Integer.parseInt(skt.nextToken());
		boolean[] control=new boolean[upperBound+1];
		
		for (int i = 0; i < numSeg; i++) {
			skt=new StringTokenizer(in.readLine());
			int a=Integer.parseInt(skt.nextToken());
			int b=Integer.parseInt(skt.nextToken());
			for (int j = a; j <= b; j++) {
				control[j]=true;
			}
			
		}
		
		int cantidad=0;
		StringBuilder stringbuilder=new StringBuilder();
		for (int i = 1; i < control.length; i++) {
			if(!control[i]) {
				cantidad++;
				stringbuilder.append(i+" ");
			}
		}
		
		out.write(cantidad+"\n");
		out.write(stringbuilder.toString().trim()+"\n");
		out.close();

	}

}