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.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class Main {

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner();
        int n=Integer.parseInt(sc.next());
        int m=Integer.parseInt(sc.next());
        boolean[] vec=new boolean[m];
        for (int i = 0; i < n; i++) {
            int x=Integer.parseInt(sc.next());
            int y=Integer.parseInt(sc.next());
            for (int j = x; j <= y; j++) {
                vec[j-1]=true;                
            }
        }
        int cant=0;
        String rta="";
        for (int i = 0; i < vec.length; i++) {
            if(!vec[i]){
                cant++;
                rta+=(i+1)+" ";
            }
        }
        System.out.println(cant);
        if(cant>0)System.out.println(rta);
    }
    

    static class Scanner {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        StringTokenizer st = new StringTokenizer("");

        int spaces = 0;

        public String nextLine() throws IOException {

            if (spaces-- > 0) {

                return "";

            } else if (st.hasMoreTokens()) {

                return new StringBuilder(st.nextToken("\n")).toString();

            }

            return br.readLine();

        }

        public String next() throws IOException {

            spaces = 0;

            while (!st.hasMoreTokens()) {

                st = new StringTokenizer(br.readLine());

            }

            return st.nextToken();

        }

        public boolean hasNext() throws IOException {

            while (!st.hasMoreTokens()) {

                String line = br.readLine();

                if (line == null) {

                    return false;

                }

                if (line.equals("")) {

                    spaces = Math.max(spaces, 0) + 1;

                }

                st = new StringTokenizer(line);

            }

            return true;

        }

    }

}