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.*;

public class MyClass {
    
    public static void main(String args[]) {
    
    
      Scanner s = new Scanner(System.in);
      int n =s.nextInt();
      int m = s.nextInt();
      int[] l = new int[n];
      int[] r = new int[n];
      int arr[] = new int[m];
      int pre[] = new int[m];
      for(int i = 0 ;i<m ; i++){
        arr[i]=0;
    }
      for(int i = 0 ;i<n ; i++){
          int p = s.nextInt();
          int y = s.nextInt();
          l[i] = p;
          r[i] = y;
      }
      for(int i = 0 ;i<n ; i++){
          for(int j = l[i] ; j<=r[i] ;j++){
              arr[j-1] = arr[j-1]+1;
          }
      }
    //   pre[0]=arr[0];
    //   for(int i = 1 ;i<=m ;i ++){
    //       pre[i] = pre[i-1]+arr[i];
    //   }
    // //   for(int i = 0 ;i<=m ;i ++){
    // //       System.out.print(pre[i]+" ");
    // //   }
      ArrayList<Integer> ar = new ArrayList<Integer>();
      for(int i=0;i<m ;i++){
          if(arr[i]==0) {ar.add(i+1);
          }
          
      }
      System.out.println(ar.size());
      for(int i=0;i<ar.size() ;i++) System.out.print(ar.get(i)+" ");
    }
}