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:
public class PointsInSegments {

    private final java.io.BufferedReader reader;
    private int segments_count, upper_bound;
    private boolean points[];

    private PointsInSegments() {
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(System.in));
    }

    private void input() throws Exception {
        String[] input = reader.readLine().split(" ");
        segments_count = Integer.parseInt(input[0]);
        upper_bound = Integer.parseInt(input[1]);
        points = new boolean[upper_bound + 1];

        for (int i = 0; i < segments_count; i++) {
            input = reader.readLine().split(" ");
            for (int j = Integer.parseInt(input[0]); j <= Integer.parseInt(input[1]); j++)
                if (!points[j])
                    points[j] = true;
        }
        
        process();
    }

    private void process() {
        int free_points = 0;
        String second_line = "";
        for (int i = 1; i <= upper_bound; i++) {
            if (!points[i]) {
                free_points++;
                second_line+=(i+" ");
            }
        }
        
        System.out.println(free_points);
        System.out.println(second_line);
    }

    public static void main(String[] args) throws Exception {
        new PointsInSegments().input();
    }
}