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.*;
import java.util.concurrent.ThreadLocalRandom;

public class Main {
	public static void main(String[] args) {
		Scanner console = new Scanner(System.in);
		int n = console.nextInt(), m = console.nextInt();
		List<Pair> segments = new ArrayList<>();
		int minl = Integer.MAX_VALUE, maxr = Integer.MIN_VALUE, sum = 0;
		List<Integer> points = new ArrayList<>();
		for(int i = 0; i < n; i++) {
			int l = console.nextInt(), r = console.nextInt();
			segments.add(new Pair(l,r));
			minl = Math.min(l, minl);
			maxr = Math.max(maxr, r);
		}
		outer: for(int i = 1; i <= m; i++) {
			for(int j = 0; j < n; j++) {
				if(segments.get(j).contains(i)) continue outer;
			}
			points.add(i);
			sum++;
		}
		
		System.out.println(sum);
		for(int i = 0; i < points.size(); i++)System.out.print(points.get(i) + " ");
		
	}
	
	static class Pair implements Comparable<Pair>{
		int l, r;
		Pair(int l, int r){
			this.l = l; 
			this.r = r;
		}
		
		public boolean contains(int i) {
			return i >= l && i <= r;
		}
		@Override
		public int compareTo(Pair o) {
			return l - o.l;
		}
		
		
	}	

	
}