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.List;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());

        List<Segment> segments = new ArrayList(n);
        for (int i = 0; i < n; ++i) {
            st = new StringTokenizer(br.readLine());
            segments.add(new Segment(Integer.parseInt(st.nextToken()), Integer.parseInt(st.nextToken())));
        }

        Collections.sort(segments);

        List<Integer> integers = new ArrayList();
        for (int i=1; i<=m; ++i) {
            boolean inside = false;
            for (int j=0;j<segments.size();++j) {
                Segment segment = segments.get(j);
                if (i >= segment.start && i <= segment.end) {
                    inside = true;
                    continue;
                } else if (i < segment.start) {
                    continue;
                }
            }
            if (!inside)
                integers.add(i);
        }

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

class Segment implements Comparable<Segment> {
    public int start;
    public int end;

    public Segment(int start, int end) {
        this.start =start;
        this.end = end;
    }

    @Override
    public int compareTo(Segment o) {
        return this.start - o.start;
    }
}