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.text.DecimalFormat;
import java.util.*;

public class solution {
	static final StdIn in = new StdIn();
	static final PrintWriter out = new PrintWriter(System.out);
	
    public static void main(String[] args) throws Exception {
    	int n = in.nextInt();
    	int m = in.nextInt();
    	int seg[] = new int[m + 1];
    	for(int i = 0; i < n; ++i) {
    		int l = in.nextInt();
    		int r = in.nextInt();
    		for(; l <= r; ++l) seg[l] = 1;
    	}
    	
    	List<Integer> ans = new ArrayList<Integer>();
    	for(int i = 1; i <= m; ++i) if(seg[i] == 0) ans.add(i);
    	out.println(ans.size());
    	for(int x : ans) out.print(x + " ");
    	out.close();
    }
    
    
    static long mul_mod(long a, long b, long m) {
    	if(a >= m) a %= m;
    	if(b >= m) b %= m;
    	double x = a;
    	long c = (long)(x * b / m);
    	long r = (long)(a * b - c * m) % m;
    	return r < 0 ? r + m : r;
    }
    
    static long pow_mod(long a, long b, long m) {
    	long res = 1;
    	a %= m;
    	while(b > 0) {
    		if(b % 2 != 0) res = mul_mod(res, a, m);
    		b >>= 1;
    		a = mul_mod(a, a, m);
    	}
    	return res;
    }
    
    static class Pair implements Comparable<Pair>{
    	public int x;
    	public int y;
    	public Pair(int a, int b) {
    		x = a;
    		y = b;
    	}
    	
    	@Override
    	public boolean equals(Object obj) {
    		Pair tmp = (Pair)obj;
    		return tmp.x == x && tmp.y == y;
    	}

    	@Override
    	public int hashCode() {
    		return x * 31 + y * 10000007;
    	}

		@Override
		public int compareTo(Pair o) {
			int d = x - o.x;
			if(d == 0) return y - o.y;
			return d;
		}
    }
    
	static class StdIn {
		final private int BUFFER_SIZE = 1 << 17;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public StdIn() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public StdIn(InputStream in) {
			try {
				din = new DataInputStream(in);
			} catch (Exception e) {
				throw new RuntimeException();
			}
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String next() {
			int c;
			while ((c = read()) != -1 && (c == ' ' || c == '\n' || c == '\r'))
				;
			StringBuilder s = new StringBuilder();
			while (c != -1) {
				if (c == ' ' || c == '\n' || c == '\r')
					break;
				s.append((char) c);
				c = read();
			}
			return s.toString();
		}

		public String nextLine() {
			int c;
			while ((c = read()) != -1 && (c == ' ' || c == '\n' || c == '\r'))
				;
			StringBuilder s = new StringBuilder();
			while (c != -1) {
				if (c == '\n' || c == '\r')
					break;
				s.append((char) c);
				c = read();
			}
			return s.toString();
		}

		public int nextInt() {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do
				ret = ret * 10 + c - '0';
			while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public int[] readIntArray(int n) {
			int[] ar = new int[n];
			for (int i = 0; i < n; ++i)
				ar[i] = nextInt();
			return ar;
		}

		public long nextLong() {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do
				ret = ret * 10 + c - '0';
			while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public long[] readLongArray(int n) {
			long[] ar = new long[n];
			for (int i = 0; i < n; ++i)
				ar[i] = nextLong();
			return ar;
		}

		public double nextDouble() {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do
				ret = ret * 10 + c - '0';
			while ((c = read()) >= '0' && c <= '9');
			if (c == '.')
				while ((c = read()) >= '0' && c <= '9')
					ret += (c - '0') / (div *= 10);
			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() {
			try {
				if (bufferPointer == bytesRead)
					fillBuffer();
				return buffer[bufferPointer++];
			} catch (IOException e) {
				throw new RuntimeException();
			}
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}
	}
}