In Berland recently a new collection of toys went on sale. This collection consists of 109 types of toys, numbered with integers from 1 to 109. A toy from the new collection of the i-th type costs i bourles.

Tania has managed to collect n different types of toys a1, a2, ..., an from the new collection. Today is Tanya's birthday, and her mother decided to spend no more than m bourles on the gift to the daughter. Tanya will choose several different types of toys from the new collection as a gift. Of course, she does not want to get a type of toy which she already has.

Tanya wants to have as many distinct types of toys in her collection as possible as the result. The new collection is too diverse, and Tanya is too little, so she asks you to help her in this.

Input

The first line contains two integers n (1 ≤ n ≤ 100 000) and m (1 ≤ m ≤ 109) — the number of types of toys that Tanya already has and the number of bourles that her mom is willing to spend on buying new toys.

The next line contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the types of toys that Tanya already has.

Output

In the first line print a single integer k — the number of different types of toys that Tanya should choose so that the number of different types of toys in her collection is maximum possible. Of course, the total cost of the selected toys should not exceed m.

In the second line print k distinct space-separated integers t1, t2, ..., tk (1 ≤ ti ≤ 109) — the types of toys that Tanya should choose.

If there are multiple answers, you may print any of them. Values of ti can be printed in any order.

Examples

Input

3 7
1 3 4


Output

2
2 5 


Input

4 14
4 6 12 8


Output

4
7 2 3 1

Note

In the first sample mom should buy two toys: one toy of the 2-nd type and one toy of the 5-th type. At any other purchase for 7 bourles (assuming that the toys of types 1, 3 and 4 have already been bought), it is impossible to buy two and more toys.
import java.util.*;
import java.io.*;
import java.awt.geom.*;
import java.math.*;

public class C {

	static final Reader in = new Reader();
	static final PrintWriter out = new PrintWriter(System.out,false);
	static boolean debug = false;

	static void solve(){
		int n = in.nextInt();
		int m = in.nextInt();
		int[] a = new int[n];
		for (int i=0; i<n; i++) {
			a[i] = in.nextInt();
		}
		Arrays.sort(a);
		ArrayList<Integer> ans = new ArrayList<>();
		long sum = 0;
		int pos = 0;
		for (int i=1; i<=1_000_000_000; i++) {
			if (pos < n && i == a[pos]) {
				pos++;
			} else {
				if (sum + i > m) break;
				sum += i;
				ans.add(i);
			}
		}
		out.println(ans.size());
		for (int i=0; i<ans.size()-1; i++) {
			out.print(ans.get(i)+" ");
		}
		if (ans.size() > 0)
			out.println(ans.get(ans.size()-1));
	}

	public static void main(String[] args) throws Exception {
		debug = args.length > 0;
		long start = System.currentTimeMillis();

		solve();
		out.flush();

		long end = System.currentTimeMillis();
		dump((end-start) + "ms");
		in.close();
		out.close();
	}

	static void dump(Object... o) { if (debug) System.err.println(Arrays.deepToString(o)); }
}

class Reader {
	private final InputStream in;
	private final byte[] buf = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	public Reader() { this(System.in);}
	public Reader(InputStream source) { this.in = source;}

	private boolean hasNextByte() {
		if (ptr < buflen) return true;
		ptr = 0;
		try{
			buflen = in.read(buf);
		}catch (IOException e) {e.printStackTrace();}
		if (buflen <= 0) return false;
		return true;
	}

	private int readByte() { if (hasNextByte()) return buf[ptr++]; else return -1;}

	private boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}

	private void skip() { while(hasNextByte() && !isPrintableChar(buf[ptr])) ptr++;}

	public boolean hasNext() {skip(); return hasNextByte();}

	public String next() {
		if (!hasNext()) throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext()) throw new NoSuchElementException();
		boolean minus = false;
		long num = readByte();

		if(num == '-'){
			num = 0;
			minus = true;
		}else if (num < '0' || '9' < num){
			throw new NumberFormatException();
		}else{
			num -= '0';
		}

		while(true){
			int b = readByte();
			if('0' <= b && b <= '9')
				num = num * 10 + (b - '0');
			else if(b == -1 || !isPrintableChar(b))
				return minus ? -num : num;
			else
				throw new NoSuchElementException();
		}
	}

	public int nextInt() {
		long num = nextLong();
		if (num < Integer.MIN_VALUE || Integer.MAX_VALUE < num)
			throw new NumberFormatException();
		return (int)num;
	}

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

	public char nextChar() {
		if (!hasNext()) throw new NoSuchElementException();
		return (char)readByte();
	}

	public String nextLine() {
		while (hasNextByte() && (buf[ptr] == '\n' || buf[ptr] == '\r')) ptr++;
		if (!hasNextByte()) throw new NoSuchElementException();

		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (b != '\n' && b != '\r') {
			sb.appendCodePoint(b);
			b = readByte();
		}

		return sb.toString();
	}

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

	public char[] nextCharArray(int n) {
		char[] res = new char[n];
		for (int i=0; i<n; i++) res[i] = nextChar();
		return res;
	}

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