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 cf184{
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m=sc.nextInt();
        IntegerPair ar[]=new IntegerPair[n];
        int i=0;
        for(i=0;i<n;i++)
        {
            int a=sc.nextInt();
            int b=sc.nextInt();
            IntegerPair temp=new IntegerPair(a,b);
            ar[i]=temp;
        }
        ArrayList<Integer> ans=new ArrayList<>();
        for(i=1;i<=m;i++)
        {
            boolean f=true;
            for(int j=0;j<n;j++)
            {
                IntegerPair temp=ar[j];
                int s=temp.first();
                int e=temp.second();
                if(i>=s&&i<=e)
                {
                    f=false;
                    break;
                }
            }
            if(f)
            {
                ans.add(i);
            }
        }
        System.out.println(ans.size());
        for(i=0;i<ans.size();i++)
        {
            System.out.print(ans.get(i)+" ");
        }
    }
}
class IntegerPair
{
    Integer f;Integer s;
    public IntegerPair(Integer a,Integer b)
    {
        f=a;
        s=b;
    }
    public Integer first()
    {
        return f;
    }
    public Integer second()
    {
        return s;
    }
}