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.*;
import java.io.*;

public class Main {

	void solve (FastScanner in, PrintWriter out) {
		
		int n = in.nextInt(), m = in.nextInt();
		int[] ar = new int[m+1];
		for (int i=0; i<n; i++) {
			int l = in.nextInt() - 1, r = in.nextInt() - 1;
			ar[l]++;
			ar[r+1]--;
		}
		
		for (int i=1; i<m+1; i++) {
			ar[i] += ar[i-1];
		}
		
		ArrayList<Integer> list = new ArrayList<>();
		for (int i=0; i<m; i++) {
			if (ar[i] == 0) list.add(i+1);
		}
		
		out.println(list.size());
		for (int i=0; i<list.size(); i++) {
			out.print((i==0?"":" ")+list.get(i));
		}
		out.println();;
		
	}
	
	void print (Object... ar) {
		System.out.println(Arrays.deepToString(ar));
	}



	public static void main(String[] args) {
		FastScanner in = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		Main main = new Main();
		main.solve(in, out);
		in.close();
		out.close();
	}

	static class FastScanner {

		private InputStream in;
		private byte[] buffer = new byte[1024];
		private  int length = 0, p = 0;

		public FastScanner (InputStream stream) {
			in = stream;
		}
		public boolean hasNextByte () {
			if (p < length) return true;
			else {
				p = 0;
				try {length = in.read(buffer);}
				catch (Exception e) {e.printStackTrace();}
				if (length <= 0) return false;
			}
			return true;
		}
		public int readByte () {
			if (hasNextByte() == true) return buffer[p++];
			return -1;
		}
		public boolean isPrintable (int n) {return 33<=n&&n<=126;}
		public void skip () {
			while (hasNextByte() && !isPrintable(buffer[p])) p++;
		}
		public boolean hasNext () {skip(); return hasNextByte();}
		public String next () {
			if (!hasNext()) throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int t = readByte();
			while (isPrintable(t)) {
				sb.appendCodePoint(t);
				t = readByte();
			}
			return sb.toString();
		}
		public String[] nextArray (int n) {
			String[] ar = new String[n];
			for (int i=0; i<n; i++) ar[i] = next();
			return ar;
		}
		public int nextInt () {return Math.toIntExact(nextLong());}
		public int[] nextIntArray (int n) {
			int[] ar = new int[n];
			for (int i=0; i<n; i++) ar[i] = nextInt();
			return ar;
		}
		public long nextLong () {
			if (!hasNext()) throw new NoSuchElementException();
			boolean minus = false;
			int temp = readByte();
			if (temp == '-') {
				minus = true;
				temp = readByte();
			}
			if (temp<'0' || '9'<temp) throw new NumberFormatException();
			long n = 0;
			while (isPrintable(temp)) {
				if ('0'<=temp && temp<='9') {
					n *= 10;
					n += temp - '0';
				}
				else throw new NumberFormatException();
				temp = readByte();
			}
			return minus? -n : n;
		}
		public double nextDouble () {
			return Double.parseDouble(next());
		}
		public void close () {
			try {in.close();}
			catch(Exception e){}
		}
	}

}