A: Information Search

problem

The posting list is a list in which there is a correspondence between the search term and the appearing document ID. For example

* Hokkaido: 1, 2, 4, 9
* Sightseeing: 1, 3, 4, 7



And so on.

From the above posting list, if you search for and, the document with ID 1, 4 will be hit, and if you search for or, ID 1, 2, 3, 4, 7, 9 will be hit.

Here, and search means "listing elements contained in either list", or search means "listing elements contained in at least one of the lists".

Since the posting list is given, output the results of and search and or search respectively.

Input format


n m
a_1 a_2 $ \ ldots $ a_n
b_1 b_2 $ \ ldots $ b_m


All inputs consist of integers.

The first line gives the lengths n and m of the two posting lists to search, separated by spaces.

The second and third lines are given the IDs contained in their respective posting lists, separated by blanks.

Constraint

* 1 \ leq n, m \ leq 2 \ times 10 ^ 5
* a_i <a_j (i <j)
* b_i <b_j (i <j)
* 1 \ leq a_i, b_i \ leq 10 ^ 9



Output format

Let A be the number of hits in the and search, and B be the number of hits in the or search.

Print on the first line in the order A B, separated by blanks.

Output the IDs hit by and search on the following line A in ascending order.

Output the IDs hit by or search on the following B line in ascending order.

Input example 1


4 4
1 2 4 9
1 3 4 7


Output example 1


2 6
1
Four
1
2
3
Four
7
9


Input example 2


4 4
1 3 5 7
2 4 6 8


Output example 2


0 8
1
2
3
Four
Five
6
7
8


Input example 3


3 5
one two Three
1 2 3 4 5


Output example 3


3 5
1
2
3
1
2
3
Four
Five






Example

Input

4 4
1 2 4 9
1 3 4 7


Output

2 6
1
4
1
2
3
4
7
9
import java.util.*;
import java.util.stream.*;
import java.io.*;
import java.math.*;

public class Main {

	static void solve (FastScanner in, PrintWriter out, Methods ms) {
		
		int n = in.nextInt(), m = in.nextInt();
		HashSet<Integer> a = new HashSet<>(), b = new HashSet<>();
		for (int i=0; i<n; i++) a.add(in.nextInt());
		for (int i=0; i<m; i++) b.add(in.nextInt());
		
		TreeSet<Integer> and = new TreeSet<>(), or = new TreeSet<>();
		
		for (Integer i : b) {
			if (a.contains(i)) and.add(i);
		}
		
		for (Integer i : a) or.add(i);
		for (Integer i : b) or.add(i);
		
		out.println(and.size() + " " + or.size());
		for (Integer i : and) out.println(i);
		for (Integer i : or) out.println(i);
		
	}



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

	static class Methods {

		public void print (Object... ar) {System.out.println(Arrays.deepToString(ar));}

		public int max (int... ar) {Arrays.sort(ar); return ar[ar.length-1];}

		public int min (int... ar) {Arrays.sort(ar); return ar[0];}

		public long gcd (long a, long b) {return b>0?gcd(b,a%b):a;}

		public long lcm (long a, long b) {return a/gcd(a,b)*b;}

		public long factorial (int i) {
			if (i==1) return 1;
			else return i*factorial(i-1);
		}

		public int manhat (int x1, int y1, int x2, int y2) {
			return Math.abs(x1-x2)+Math.abs(y1-y2);
		}

		public double euclid (double x1, double y1, double x2, double y2) {
			return Math.sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
		}

		public boolean isPrime (int n) {
			if (n==2) return true;
			if (n<2 || n%2==0) return false;
			for (int i=3; i<=Math.sqrt(n); i+=2) if(n%i==0) return false;
			return true;
		}

	}

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

		public double nextDouble () {
			return Double.parseDouble(next());
		}

		public double[] nextDoubleArray (int n) {
			double[] ar = new double[n];
			for (int i=0; i<n; i++) ar[i] = nextDouble();
			return ar;
		}

		public void close () {
			try {in.close();}
			catch(Exception e){}
		}

	}

}
