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.io.*;import java.math.*;

//=============================================================================
//--------------------------Main-Class---------------------------------
//=============================================================================

public class A {

	public static void process()throws IOException{
		
		int n = sc.nextInt(),m = sc.nextInt();
		int freq[] = new int[m+1];
		for(int i=0; i<n; i++) {
			int a = sc.nextInt(),b = sc.nextInt();
			for(int j=a; j<=b;j++)freq[j]++;
		}
		ArrayList<Integer> lis = new ArrayList<Integer>();
		for(int i=1; i<=m; i++) {
			if(freq[i] == 0)lis.add(i);
		}
		System.out.println(lis.size());
		for(int e : lis)System.out.print(e+" ");
		
		
    }
	

	//=============================================================================
	//--------------------------Dheeraj-Bhagchandani---------------------------------
	//=============================================================================
  
	 
    static FastScanner sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        boolean oj = true;
        if(oj){sc=new FastScanner();out=new PrintWriter(System.out);}
        else{sc=new FastScanner(100);out=new PrintWriter("output.txt");}
        int t=1;
//        t = sc.nextInt();
        while(t-->0) {process();}
        out.flush();out.close();  
    }
    
    static class Pair implements Comparable<Pair> {
		int y;
		long x;
		Pair(long x, int y) {
			this.x = x;
			this.y = y;
		}
		@Override
		public int compareTo(Pair o) {
			return Long.compare(this.x, o.x);
		}
	}
    
/////////////////////////////////////////////////////////////////////////////////////////////////////////
    
	static void println(Object o){out.println(o);}
	static void println(){out.println();}
	static void print(Object o){out.print(o);}
	static void pflush(Object o){out.println(o);out.flush();}
	static int ceil(int x, int y) {return (x % y == 0 ? x / y : (x / y + 1));}
	static long ceil(long x, long y) {return (x % y == 0 ? x / y : (x / y + 1));}
	static int max(int x, int y) {return Math.max(x, y);}
	static int min(int x, int y) {return Math.min(x, y);}
	static int abs(int x) {return Math.abs(x);}
	static long abs(long x) {return Math.abs(x);}
	static int log2(int N) {int result = (int) (Math.log(N) / Math.log(2));return result;}
	static long max(long x, long y) {return Math.max(x, y);}
	static long min(long x, long y) {return Math.min(x, y);}
	public static int gcd(int a, int b) {
	BigInteger b1 = BigInteger.valueOf(a);BigInteger b2 = BigInteger.valueOf(b);
	BigInteger gcd = b1.gcd(b2);return gcd.intValue();}
	public static long gcd(long a, long b) {
	BigInteger b1 = BigInteger.valueOf(a);BigInteger b2 = BigInteger.valueOf(b);
	BigInteger gcd = b1.gcd(b2);return gcd.longValue();}
   
	
	
/////////////////////////////////////////////////////////////////////////////////////////////////////////
	
	static class FastScanner{BufferedReader br; StringTokenizer st;
	FastScanner()throws FileNotFoundException{
    	br=new BufferedReader(new InputStreamReader(System.in));}
	FastScanner(int a)throws FileNotFoundException{
   	br = new BufferedReader(new FileReader("input.txt"));}
    String next()throws IOException{
    while (st == null || !st.hasMoreElements()) {try{
    st = new StringTokenizer(br.readLine());}
    catch (IOException  e){ e.printStackTrace(); }}
    return st.nextToken(); } int nextInt() throws IOException{
    return Integer.parseInt(next());}
    long nextLong() throws IOException
    {return Long.parseLong(next());}
    double nextDouble()throws IOException { return Double.parseDouble(next()); }
    String nextLine() throws IOException{ String str = ""; try{
    str = br.readLine();} catch (IOException e){
    e.printStackTrace();} return str;}
    int[] readArray(int n)throws IOException{int[]A=new int[n];
    for(int i=0;i!=n;i++){A[i]=sc.nextInt();}return A;}
    long[] readArrayLong(int n)throws IOException{long[]A=new long[n];
    for(int i=0;i!=n;i++){A[i]=sc.nextLong();}return A;}}
	
	static void ruffleSort(int[] a) {Random get = new Random();
		for (int i = 0; i < a.length; i++) {int r = get.nextInt(a.length);
		int temp = a[i];a[i] = a[r];a[r] = temp;}Arrays.sort(a);}
	static void ruffleSort(long[] a) {Random get = new Random();
		for (int i = 0; i < a.length; i++) {int r = get.nextInt(a.length);
		long temp = a[i];a[i] = a[r];a[r] = temp;}Arrays.sort(a);}
}