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:
//Author: Patel Rag
//Java version "1.8.0_211"
import java.util.*;
import java.io.*;

public class Main
{
  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()); }

    float nextFloat() { return Float.parseFloat(next()); }

    boolean nextBoolean() { return Boolean.parseBoolean(next()); }

    String nextLine()
    {
      String str = "";
      try
      {
        str = br.readLine();
      }
      catch (IOException e)
      {
        e.printStackTrace();
      }
      return str;
    }
  }
  static long modExp(long x, long n, long mod)    //binary Modular exponentiation
  {
    long result = 1;
    while(n > 0)
    {
        if(n % 2 == 1)
            result = (result%mod * x%mod)%mod;
        x = (x%mod * x%mod)%mod;
        n=n/2;
    }
    return result;
  }
  static long gcd(long a, long b)
  {
    if(a==0) return b;
    return gcd(b%a,a);
  }
  public static void main(String[] args)
  throws IOException
  {
    FastReader fr = new FastReader();
    int n = fr.nextInt();
    int m = fr.nextInt();
    boolean[] vis = new boolean[m+1];
    Arrays.fill(vis,false);
    for(int i = 0; i < n; i++)
    {
      int l = fr.nextInt();
      int r = fr.nextInt();
      for(int j = l; j <= r; j++)
      {
        if(!vis[j]) vis[j] = true;
      }
    }
    Vector<Integer> out = new Vector<>(n);
    for(int i = 1; i <= m; i++)
    {
      if(!vis[i])
      {
        out.add(i);
      }
    }
    System.out.println(out.size());
    for(int i = 0 ; i < out.size(); i++)
    {
      System.out.print(out.get(i) + " ");
    }

  }
}
class Pair<U, V>  // Pair class
{
    public final U first;       // first field of a Pair
    public final V second;      // second field of a Pair

    private Pair(U first, V second)
    {
      this.first = first;
      this.second = second;
    }

    @Override
    public boolean equals(Object o)
    {
      if (this == o) return true;

      if (o == null || getClass() != o.getClass()) return false;

      Pair<?, ?> pair = (Pair<?, ?>) o;

      if (!first.equals(pair.first)) return false;
      return second.equals(pair.second);
    }

    @Override
    public int hashCode()
    {
      return 31 * first.hashCode() + second.hashCode();
    }

    public static <U, V> Pair <U, V> of(U a, V b)
    {
      return new Pair<>(a, b);
    }
}
class myComp implements Comparator<Pair>
{
  public int compare(Pair a,Pair b)
  {
    if(a.first != b.first) return ((int)a.first - (int)b.first);
    if(a.second != b.second) return ((int)a.second - (int)b.second);
    return 0;
  }
}
class BIT       //Binary Indexed Tree aka Fenwick Tree
{
  public long[] m_array;

  public BIT(long[] dat)
  {
    m_array = new long[dat.length + 1];
    Arrays.fill(m_array,0);
    for(int i = 0; i < dat.length; i++)
    {
      m_array[i + 1] = dat[i];
    }
    for(int i = 1; i < m_array.length; i++)
    {
      int j = i + (i & -i);
      if(j < m_array.length)
      {
        m_array[j] = m_array[j] + m_array[i];
      }
    }
  }

  public final long prefix_query(int i)
  {
    long result = 0;
    for(++i; i > 0; i = i - (i & -i))
    {
      result = result + m_array[i];
    }
    return result;
  }

  public final long range_query(int fro, int to)
  {
    if(fro == 0)
    {
      return prefix_query(to);
    }
    else
    {
      return (prefix_query(to) - prefix_query(fro - 1));
    }
  }

  public void update(int i, long add)
  {
    for(++i; i < m_array.length; i = i + (i & -i))
    {
      m_array[i] = m_array[i] + add;
    }
  }
}