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.Arrays;
import java.util.StringTokenizer;

public class PointsinSegments {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	String s=br.readLine();
	StringTokenizer st=new StringTokenizer(s);
	int n=Integer.parseInt(st.nextToken());
	int m=Integer.parseInt(st.nextToken());
	
	boolean [] x=new boolean[m+1];
	Arrays.fill(x, true);
	x[0]=false;
	for(int i=0;i<n;i++) {
		st=new StringTokenizer(br.readLine());
		int f=Integer.parseInt(st.nextToken());
		int l=Integer.parseInt(st.nextToken());
	
		for(int j=f;j<=l;j++) {
				x[j]=false;	
				
		}
	}
	int a=0;
	for(int i=0;i<m+1;i++) {
		if (x[i])
			a++;	
	}
	System.out.println(a);
	for(int i=0;i<m+1;i++) {
		if (x[i])
			System.out.print(i+" ");
		
	}
	}

}