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.util.*;
import java.io.BufferedWriter;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;

public class A1015 {
    static class OutputWriter {
        private final PrintWriter writer;
    
        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }
    
        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }
    
        public void print(int[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0)
                    writer.print(' ');
                writer.print(array[i]);
            }
        }
    
        public void printLine(int[] array) {
            print(array);
            writer.println();
        }
    
        public void close() {
            writer.close();
        }
    
    }
    static class Pair {
        int value;
        int index;
        Pair(int value, int index) {
            this.value = value;
            this.index = index;
        }
    }
    static class MyComparator implements Comparator<Pair> {
        @Override
        public int compare(Pair p1, Pair p2) {
            if (p1.value != p2.value) return p1.value - p2.value;
            return p1.index - p2.index;
        }
    }
    public static void main(String[] args) {
		OutputStream outputStream = System.out;
        OutputWriter out = new OutputWriter(outputStream);
        Scanner sc=  new Scanner(System.in);
        //BufferedReader br = new BufferedReader(new InputStreamReader(System.in));


        int n = sc.nextInt();
        int m = sc.nextInt();

        int[] arr = new int[m+1];
        List<Integer> list = new ArrayList<>();
        for (int i=0; i<n; i++) {
            int l = sc.nextInt();
            int r= sc.nextInt();
            for (int j=l; j<=r; j++) arr[j] = 1;
        }
        int ans = 0;
        for (int i=1; i<=m; i++) {
            if (arr[i] == 0) {
                ans++;
                list.add(i);
            }
        }        
        System.out.println(ans);
        for (int i : list) {
            System.out.print(i + " ");
        }
		//int n = in.readInt();
        //int[] temparr = IOUtils.readIntArray(in, n);
        //int[] rating = new int[n];
        //out.printLine(rating);
        //System.out.println(ans);
        out.close();
    }
}