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.Scanner; 
import java.util.StringTokenizer; 
import java.util.*;
  
public class div3_praca
{ 
    //By shwetank_verma
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
    static int mod=1000000007;
    static boolean primes[]=new boolean[1000007];
    static ArrayList<Integer> b=new ArrayList<>();
    static boolean seive(int n){
        Arrays.fill(primes,true);
        primes[0]=primes[1]=false;
        for(int i=2;i*i<=n;i++){
            if(primes[i]==true){
                for(int p=i*i;p<=n;p+=i){
                    primes[p]=false;
                }
            }
        }
        if(n<1000007){
        	for(int i=2;i<=n;i++) {
        		if(primes[i])
        			b.add(i);
        	}
            return primes[n];
        }
        return false;
        
    }
    static int gcd(int a,int b){
        if(b==0)
        return a;
        return gcd(b,a%b);
    }
    static long GCD(long a,long b){
        if(b==0)
        return a;
        return GCD(b,a%b);
    }
    static ArrayList<Integer> segseive(int l,int r){
    	
    	ArrayList<Integer> isprime=new ArrayList<Integer>();
    	boolean p[]=new boolean[r-l+1];
    	Arrays.fill(p, true);
        
    	for(int i=0;b.get(i)*b.get(i)<=r;i++) {
    		int currprime=b.get(i);
    		int base=(l/currprime)*currprime;
    		if(base<l) {
    			base+=currprime;
    		}
    		for(int j=base;j<=r;j+=currprime) {
    			p[j-l]=false;
    		}
    		
    		
    		if(base==currprime) {
    			p[base-l]=true;
    		}
    		
    	}
    	for(int i=0;i<=r-l;i++) {
    		if(p[i])
    			isprime.add(i+l);
    	}
    	return isprime;
    }
      static int LowerBound(int a[], int x) { // x is the target value or key
  int l=-1,r=a.length;
  while(l+1<r) {
    int m=(l+r)>>>1;
    if(a[m]>=x) r=m;
    else l=m;
  }
  return r;
}
static int UpperBound(int a[], int x) {// x is the key or target value
    int l=-1,r=a.length;
    while(l+1<r) {
       int m=(l+r)>>>1;
       if(a[m]<=x) l=m;
       else r=m;
    }
    return l+1;
 }

  
    public static void main(String[] args) 
    { 
        FastReader sc=new FastReader(); 
        try{
           
                int n=sc.nextInt();
                int s=n;
                int m=sc.nextInt();
                HashSet<Integer> hs=new LinkedHashSet();
                while(s-->0) {
                	int l=sc.nextInt();
                	int r=sc.nextInt();
                	for(int i=l;i<=r;i++) {
                		hs.add(i);
                	}
                }
                StringBuilder sb=new StringBuilder();
                int size=0;
                for(int i=1;i<=m;i++) {
                	if(hs.contains(i)) {
                		
                	}
                	else {
                		sb.append(i+" ");
                		size++;
                	}
                }
                System.out.println(size);
                System.out.println(sb);
           
            
        }catch(Exception e){
            return;
        }
    } 
}