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.Comparator;
import java.util.StringTokenizer;

public class NewMain {
    public static class P {
        int n ,m;
        public P(int n, int m) {
            this.n = n;
            this.m = m;
        }
        public P() {
        }
    }
       
    public static void main(String[] args) throws IOException {
        BufferedReader L=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer l=new StringTokenizer(L.readLine());
        int n=Integer.parseInt(l.nextToken());
        int m1=Integer.parseInt(l.nextToken());
        int m[]=new int[m1+1];
        
        for (int i = 0; i <m.length; i++) {
            m[i]=i;
        }
        
        P a[]=new P[n];
        for (int i = 0; i <n; i++) {
            l=new StringTokenizer(L.readLine());
            int a1=Integer.parseInt(l.nextToken());
            int a2=Integer.parseInt(l.nextToken());
            a[i]=new P(a1, a2);
        }
        Arrays.sort(a,Comparator.comparing((P p)->p.n));
        for (int i = 0; i <n; i++) {
            int x=Math.abs(a[i].n-a[i].m);
            int x1=a[i].n;
                for (int j = 0; j <= x; j++) {
                    m[x1]=0;
                    x1+=1;
                }
        }
        int count=0;String number="";
        for (int i = 0; i < m.length; i++) {
            if (m[i]==0) {}
            else{
                count++;
                number=m[i]+" "+number;
            }   
        }
        System.out.println(count);
        System.out.println(number);
    }
}