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.util.ArrayList;
import java.util.List;
import java.util.Scanner;


public class Solution
{
    public static void main( String[] args)
    {
        Scanner scan = new Scanner(System.in);
        int n, m;
        n = scan.nextInt();
        m = scan.nextInt();

        int markl[] = new int[m+1];
        int markr[] = new int[m+1];
        for(int i = 0; i < m+1; i++) {
            markl[i] = 0;
            markr[i] = 0;
        }

        for(int i = 0; i < n; i++) {
            int l,r;
            l = scan.nextInt();
            r = scan.nextInt();
            markl[l]++;
            markr[r]++;
        }

        int count = 0;
        int result = 0;
        List<Integer> lists = new ArrayList<Integer>();
        for(int i = 1; i <= m; i++){
            if(count == 0 && markl[i] == 0 && markr[i] == 0) {
                result++;
                lists.add(i);
                continue;
            }

            if(markl[i] > 0) {
                count += markl[i];
            }

            if(markr[i] > 0) {
                count -= markr[i];
            }
        }

        System.out.println(result);
        if(result > 0) {
            StringBuilder sb = new StringBuilder();
            sb.append(lists.get(0));
            for(int i = 1; i < result; i++){
                sb.append(" ").append(lists.get(i));
            }
            System.out.println(sb.toString());
        }
    }
}