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.*;
public class A_B_and_team_trainin{
	
	

	public static void main(String[] args) {
Scanner scn=new Scanner(System.in);
int n=scn.nextInt();
int m=scn.nextInt();
int arr[]=new int[m];
for(int i=0;i<n;i++){
	int u=scn.nextInt()-1;
	int v=scn.nextInt()-1;
	arr[u]+=1;
	if(v+1<m){
		arr[v+1]+=-1;
	}
}
int sum=arr[0];
for(int i=1;i<m;i++){
	sum+=arr[i];
	arr[i]=sum;
}
ArrayList<Integer> al=new ArrayList<>();
for(int i=0;i<m;i++){
	if(arr[i]==0){
		al.add(i);
	}
}
System.out.println(al.size());
for(int i=0;i<al.size();i++)
System.out.print((al.get(i)+1)+" ");
System.out.println();
		
	}
	}