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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class A {

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String line = br.readLine().trim(), buffer[];
        buffer = line.split("\\s+");
        int N = Integer.parseInt(buffer[0]);
        int M = Integer.parseInt(buffer[1]);
        boolean used[] = new boolean[M];
        int count = M;
        for (int i = 0; i < N; i++) {
            line = br.readLine().trim();
            buffer = line.split("\\s+");
            int a = Integer.parseInt(buffer[0]) - 1;
            int b = Integer.parseInt(buffer[1]) - 1;

            for (int j = a; j <= b; j++) {
                if (!used[j]) {
                    count--;
                    used[j] = true;
                }
            }
        }
        System.out.println(count);
        if (count > 0) {
            boolean started = false;
            for (int j = 0; j < M; j++) {
                if (started) {
                    System.out.print(" ");
                }
                if (!used[j]) {
                    started = true;
                    System.out.print(j + 1);
                }
            }
            System.out.println("");
        }

    }
}
/*
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class A {

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    }
}
 */