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 static java.lang.Integer.parseInt;
import static java.util.Arrays.sort;

public class A_Points_in_Segments {
    static class pair{
        int l,r;
        public pair(int l,int r){
            this.l = l;
            this.r = r;
        }
    }
    static int n,m;
    static pair p[];
    static ArrayList<Integer> ans;
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer tk = new StringTokenizer(in.readLine());
        n = parseInt(tk.nextToken());
        m = parseInt(tk.nextToken());
        p = new pair[n];
        ans = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            tk = new StringTokenizer(in.readLine());
            int l,r;
            l = parseInt(tk.nextToken());
            r = parseInt(tk.nextToken());
            p[i] = new pair(l,r);
        }
        sort(p,Comparator.comparing((pair p) -> p.l));
        if(p[0].l > 1)
            for (int i = 1; i < p[0].l; i++)
                ans.add(i);

        int max = p[0].r;
        for (int i = 1; i < n; i++) {
            if(p[i - 1].r < p[i].l && p[i].l > max){
                for (int j = max + 1; j < p[i].l; j++) {
                    ans.add(j);
                }
            }
            max = Math.max(max,p[i].r);
        }
        if(max < m)
            for (int i = max + 1; i <= m; i++)
                ans.add(i);

        System.out.println(ans.size());
        if(ans.size() == 0)
            return;
        System.out.print(ans.get(0));
        for (int i = 1; i < ans.size(); i++) {
            System.out.print(" "+ans.get(i));
        }
    }
}