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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ADiv3_501Task solver = new ADiv3_501Task();
        solver.solve(1, in, out);
        out.close();
    }

    static class ADiv3_501Task {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            int rng = in.nextInt();
//        System.out.println(n + " " + rng);

            int[][] matrix = new int[n][2];
            int[] result = new int[rng + 1];
            for (int i = 1; i <= rng; i++) {
                result[i] = i;
            }
            int count = rng;
            for (int i = 0; i < n; i++) {
                int l = in.nextInt();
                int r = in.nextInt();
                for (int j = l; j <= r; j++) {
                    if (result[j] != -1) {
                        result[j] = -1;
                        count--;
                    }
                }
            }
            out.print(count + "\n");
            //out.println("");
            boolean flag = true;
            if (count > 0) {
                for (int i = 1; i <= rng; i++) {
                    if (result[i] > 0) {
                        if (flag) flag = false;
                        else out.print(" ");
                        out.print(result[i]);
                    }
                }
            }

        }

    }
}