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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {


    public static void main(String[] args) {

        try (
                BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
                PrintWriter output = new PrintWriter(System.out)
        ) {
            // read number of line segments and upper coordinate bound
            String theFirstLine = input.readLine();
            Scanner sc = new Scanner(theFirstLine);

            int numLineSegments = sc.nextInt();
            int upperCoordBound = sc.nextInt();

            // read line segments
            int[] pointsArr = new int[upperCoordBound];
            for (int i = 0; i < numLineSegments; i++) {
                String line = input.readLine();
                sc = new Scanner(line);
                int firstPoint = sc.nextInt();
                int secondPoint = sc.nextInt();
                for (int j = firstPoint; j <= secondPoint; j++) {
                    pointsArr[j - 1] = 1;
                }
            }

            int resultPointsCount = 0;
            List<Integer> resultPoints = new ArrayList<>();

            for (int i = 0; i < upperCoordBound; i++) {
                if (pointsArr[i] == 0) {
                    resultPointsCount++;
                    resultPoints.add(i + 1);
                }
            }

            System.out.println(resultPointsCount);
            resultPoints.stream().forEach(x -> System.out.print(x + " "));

        } catch (IOException ex) {
            // nothing to do
        }
    }

}