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.*;
import java.util.*;

import static java.lang.Math.*;

public class Main implements Runnable {
    public static void main(String[] args) throws IOException, InterruptedException {
        //System.setIn(new FileInputStream("input.txt"));
        //System.setOut(new PrintStream(new FileOutputStream("output.txt")));
        Thread t = new Thread(null, new Main(), "solutionThread", 1 << 28);
        t.start();
    }

    @Override
    public void run() {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        int[] ar = new int[m+1];
        for (int i = 0; i < n; i++) {
            int l = scanner.nextInt();
            int r = scanner.nextInt();
            for (int j = l; j <= r; j++) {
                ar[j] = 1;
            }
        }
        List<Integer> ans = new ArrayList<>();
        for (int i = 1; i <= m; i++) {
            if (ar[i]==0) ans.add(i);
        }
        System.out.println(ans.size());
        ans.forEach( i -> System.out.printf("%d ", i));
    }
}
/*


class Scanner {
    private final BufferedReader br = new BufferedReader( new InputStreamReader( System.in ) );
    private StringTokenizer st = new StringTokenizer( "" );
    public Scanner( InputStream in ) {}
    public String next() {
        while ( !st.hasMoreElements() )
            try {
                st = new StringTokenizer( br.readLine() );
            } catch ( IOException e ) {
                e.printStackTrace();
            }
        return st.nextToken();
    }
    public int nextInt() { return Integer.parseInt( next() ); }
    public long nextLong() { return Long.parseLong( next() ); }
    public int[] readArray( int n ) {
        int[] a = new int[ n ];
        for ( int i = 0; i < n; i++ ) {
            a[ i ] = nextInt();
        }
        return a;
    }
    public double nextDouble() { return Double.parseDouble( next() ); }
}

class System {
    public static final InputStream in = java.lang.System.in;
    public static final PrintStream out = new PrintWriter(java.lang.System.out);
}

*/