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.math.*;
import static java.lang.System.out;

public class CF1015A
{
    public static void main(String[] args) throws IOException
    {
        //BufferedReader f = new BufferedReader(new FileReader("/Users/spencersharp/Desktop/input.txt"));
        
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        //PrintWriter writer = new PrintWriter(new BufferedOutputStream(System.out));
        
        String output = ""; //Write all output to this string

        //Code here
        StringTokenizer st;
        st = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        int[] starts = new int[n];
        int[] ends = new int[n];
        
        
        for(int i = 0; i < n; i++)
        {
            st = new StringTokenizer(f.readLine());
            starts[i] = Integer.parseInt(st.nextToken());
            ends[i] = Integer.parseInt(st.nextToken());
        }
        
        ArrayList<Integer> resultPoints = new ArrayList<Integer>();
        for(int i = 1; i <= m; i++)
        {
            boolean found = false;
            for(int j = 0; j < n; j++)
            {
                if(starts[j] <= i && i <= ends[j])
                {
                    found = true;
                }
            }
            if(!found)
            {
                resultPoints.add(i);
            }
        }
        out.println(resultPoints.size());
        for(int i = 0; i < resultPoints.size(); i++)
        {
            out.print(resultPoints.get(i) + " ");
        }
        out.println();
        
        /*
        writer.println(output);
        writer.close();
        System.exit(0);
        */
    }
}