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.io.*;
import java.math.BigInteger;
import java.util.*;


public class Main
{
	private InputStream is;
	private PrintWriter out;
	int time = 0, freq[], start[], end[], dist[], black[], MOD = (int) (1e9 + 7), arr[], weight[][], x[], y[], parent[];
	int MAX = 1000001, N, K;
	long red[], ans = Long.MAX_VALUE;

	ArrayList<Integer>[] amp;
	ArrayList<Pair>[] pmp;
	boolean b[];
	boolean boo[][], b1[];
	Pair prr[];
	HashMap<Pair, Integer> hm = new HashMap();
	int Dp[][] = new int[1100][1100];

	void soln() 
	{
		is = System.in;
		out = new PrintWriter(System.out);
		long s = System.currentTimeMillis();
		solve();

		// out.close();
		out.flush();
		// tr(System.currentTimeMillis() - s + "ms");
	}

	static class ST1 // min ST
	{
		long arr[], st[];
		int size;

		ST1(long a[]) {
			arr = a.clone();
			size = 10 * arr.length;
			st = new long[size];
			build(0, arr.length - 1, 1);
		}

		void build(int ss, int se, int si) {
			if (ss == se) {
				st[si] = arr[ss];
				return;
			}
			int mid = (ss + se) / 2;
			int val = 2 * si;
			build(ss, mid, val);
			build(mid + 1, se, val + 1);
			st[si] = Math.min(st[val], st[val + 1]);
		}

		void update(int ss, int se, int idx, long val, int si) {
			if (ss == se) {
				// if(si==idx+1)
				st[si] = val;
				return;
			}
			int mid = (ss + se) / 2;
			if (ss <= idx && idx <= mid) {
				update(ss, mid, idx, val, 2 * si);
			} else {
				update(mid + 1, se, idx, val, 2 * si + 1);
			}
			int v = 2 * si;
			st[si] = Math.min(st[v], st[v + 1]);
		}

		long get(int ss, int se, int l, int r, int si) {
			if (l > se || r < ss || l > r)
				return Long.MAX_VALUE / 1000;
			if (l <= ss && r >= se)
				return st[si];
			int mid = (ss + se) / 2;
			int val = 2 * si;
			return Math.min(get(ss, mid, l, r, val), get(mid + 1, se, l, r, val + 1));
		}
	}

	public static void main(String[] args) throws Exception
	{
		new Thread(null, new Runnable() 
		{
			public void run() 
			{
				try 
				{
					// new CODEFORCES().soln();
				} catch (Exception e) 
				{
					System.out.println(e);
				}
			}
		}, "1", 1 << 26).start();
		new Main().soln();
	}

	int D[][];
	char ch[][], ch1[];
	int hash = 29;
	int x2, y2;
	HashSet<Integer>[] hs = (HashSet<Integer>[]) new HashSet[110];
	cell[] c;
	Pair[] p = new Pair[4];
	HashSet<String> set = new HashSet<>();
	HashSet<String> dp = new HashSet<>();
	private void solve()
	{
		int n = ni(), m = ni();
		int arr[] = na(n);
		HashSet<Integer> hs = new HashSet<>();
		for(int i: arr) hs.add(i);
		long ans = 0;
		ArrayList<Integer> amp = new ArrayList<>();
		for(int i = 1;i<=5000000;i++) {
			if(hs.contains(i)) continue;
			if(ans>=m) break;
			else {
				if((ans+i)<=m) {
					ans += i;
					amp.add(i);
				}
				else break;
			}
		}
		out.println(amp.size());
		for(int i : amp) out.print(i+" ");
	}
	void bfs(int s, int n) {
		b = new boolean[n];
		dist = new int[n];
		Arrays.fill(dist, 1000000);
		dist[s] = 0;
		b[s] = true;
		Queue<Integer> q = new LinkedList<>();
		q.add(s);
		while(!q.isEmpty()) {
			int y = q.poll();
			for(int i : amp[y]) {
				dist[i] = min(dist[i],dist[y]+1);
				if(!b[i]) {
					b[i] = true;
					q.add(i);
				}
			}
		}
	}
	boolean check(String s, String s1) {
		char ch1[] = s.toCharArray(), ch2[] = s1.toCharArray();
		int arr[] = new int[10];
		for(char c : ch1) {
			arr[c-'0']++;
		}
		int ans = 0;
		for(char c:ch2) {
			arr[c-'0']--;
		}
		
		for(int i:arr) ans += ((i>0)?i:0);
		return ans==3;
	}
	void seive(int n)
	{
		start = new int[n];
		for(int i = 2;i<n;i++) {
			if(start[i]==0) {
				for(int j = 2*i;j<n;j+=i) {
					start[j] = i;
				}
			}
		}
	}
	void print(int[][] arr) 
	{
		int seed = 110, n = arr.length - 220;
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				System.out.print(arr[i + seed][j + seed] + " ");
			}
			System.out.println();
		}
		System.out.println();
	}

	 class cell implements Comparable<cell>
	 {
		int s, d, p, i;

		cell(int t, int d, int p, int i) {
			this.s = t;
			this.p = p;
			this.d = d;
			this.i = i;
		}

		public int compareTo(cell other) {
			// return Integer.compare(val, other.val);
			return Long.compare(d, other.d) != 0 ? (Long.compare(d, other.d)): (Long.compare(i,other.i));
											// other.v));//((Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)):
											// (Long.compare(v, other.v)))
			// &(Long.compare(u, other.v) != 0 ? (Long.compare(u, other.v)):
			// (Long.compare(v, other.u))));
		}

		public String toString() {
			return this.d + " " + this.s +" "+this.p+" "+this.i;
		}
	}

	int abs(int x)
	{
		return ((x > 0) ? x : -x);
	}

	long ret(int p) 
	{
		if (p >= 0)
			return 0;
		else
			return 1;
	}

	long val(int p, int a, int b) 
	{
		if (p >= 0) {
			return (a * 1l * p);
		}
		return (b * 1l * p);
	}

	void ternary_search(int l, int r) 
	{
		// System.out.println(l+" "+r+" "+ans);
		// for(int i : arr) System.out.print(i+" ");
		// System.out.println();
		if (r >= l) {
			int mid1 = l + (r - l) / 3;
			int mid2 = r - (r - l) / 3;
			long cnt1 = 0, cnt2 = 0;
			cnt1 = compute(mid1);
			cnt2 = compute(mid2);
			// System.out.println(mid1+" "+ cnt1+" "+mid2+" "+cnt2);
			ans = Math.min(cnt1, cnt2);
			if (cnt1 < cnt2) {
				ternary_search(l, mid2 - 1);
			} else {
				ternary_search(mid1 + 1, r);
			}
		}
		return;
	}

	long compute(int x) 
	{
		long ans = 0;
		int c = arr[0];
		for (int i = 1; i <= x; i++) {
			ans += max(c + 1 - arr[i], 0);
			c = max(c + 1, arr[i]);
		}
		int temp = arr[x];
		arr[x] = max(c + 1, arr[x]);
		// SSystem.out.println(arr[x]+" "+ans);
		c = arr[arr.length - 1];
		for (int i = arr.length - 1; i > x; i--) {
			ans += max(c + 1 - arr[i - 1], 0);
			c = max(c + 1, arr[i - 1]);
		}
		arr[x] = temp;
		return ans;
	}

	public int getParent(int x) 
	{
		while (parent[x] != x) {
			parent[x] = parent[parent[x]];
			x = parent[x];
		}
		return x;
	}

	void getFactors(int n, int x)
	{
		for (int i = 1; i * i <= n; i++) {
			if (n % i == 0) {
				hs[x].add(i);
				hs[x].add(n / i);
			}
		}
	}

	void recur(int a, int b, int k) 
	{
		if (k == 0) {
			if (a == x2 && b == y2)
				ans++;
			return;
		}
		recur(a, b + 1, k - 1);
		recur(a, b - 1, k - 1);
		recur(a + 1, b, k - 1);
		recur(a - 1, b, k - 1);
	}

	int min(int a, int b) 
	{
		return (a < b) ? a : b;
	}

	/*private class Cell implements Comparable<Cell> {
		int u, v, s;

		public Cell(int u, int v, int s) {
			this.u = u;
			this.v = v;
			this.s = s;
		}

		public int hashCode() {
			return Objects.hash();
		}

		public int compareTo(Cell other) {
			return (Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s))
					: (Long.compare(v, other.v) != 0 ? Long.compare(v, other.v) : Long.compare(u, other.u)))
					& ((Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s))
							: (Long.compare(u, other.v) != 0 ? Long.compare(u, other.v) : Long.compare(v, other.u))));
		}

		public String toString() {
			return this.u + " " + this.v;
		}
	}*/

	class Pair implements Comparable<Pair>
	{
		int u ,v,i;

		Pair(int u, int v) {
			this.u = u;
			this.i = v;
		}

		Pair(int u, int v, int i) {
			this.u = u;
			this.v = v;
			this.i = i;
		}

		public int hashCode() {
			return Objects.hash();
		}

		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return ((u == other.u && v == other.v));
		}

		public int compareTo(Pair other) {
			// return Integer.compare(val, other.val);
			return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(i, other.i));// ((Long.compare(u,
		
		}									
		public String toString() {
			return this.u + " " + this.v +" "+this.i;
		}
	}

	int max(int a, int b) 
	{
		if (a > b)
			return a;
		return b;
	}

	static class FenwickTree 
	{

		int[] array; // 1-indexed array, In this array We save cumulative
						// information to perform efficient range queries and
						// updates

		public FenwickTree(int size) {
			array = new int[size + 1];
		}

		public int rsq(int ind) {
			assert ind > 0;
			int sum = 0;
			while (ind > 0) {
				sum += array[ind];
				// Extracting the portion up to the first significant one of the
				// binary representation of 'ind' and decrementing ind by that
				// number
				ind -= ind & (-ind);
			}
			return sum;
		}

		public int rsq(int a, int b) {
			assert b >= a && a > 0 && b > 0;
			return rsq(b) - rsq(a - 1);
		}

		public void update(int ind, int value) {
			assert ind > 0;
			while (ind < array.length) {
				array[ind] += value;
				// Extracting the portion up to the first significant one of the
				// binary representation of 'ind' and incrementing ind by that
				// number
				ind += ind & (-ind);
			}
		}

		public int size() {
			return array.length - 1;
		}
	}

	void buildGraph(int n)
	{
		for (int i = 0; i < n; i++) {
			int x1 = ni(), y1 = ni(), z = ni();
			//pmp[x1].add(new Pair(y1, z));
		}
	}

	long modInverse(long a, long mOD2)
	{
		return power(a, mOD2 - 2, mOD2);
	}

	long power(long x, long y, long m) 
	{
		if (y == 0)
			return 1;
		long p = power(x, y / 2, m) % m;
		p = (p * p) % m;

		return (y % 2 == 0) ? p : (x * p) % m;
	}

	public long gcd(long a, long b)
	{
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	static class ST 
	{
		int arr[], lazy[], n;

		ST(int a) {
			n = a;
			arr = new int[10 * n];
			lazy = new int[10 * n];
		}

		void up(int l, int r, int val) {
			update(0, n - 1, 0, l, r, val);
		}

		void update(int l, int r, int c, int x, int y, int val) {
			if (lazy[c] != 0) {
				lazy[2 * c + 1] += lazy[c];
				lazy[2 * c + 2] += lazy[c];
				if (l == r)
					arr[c] += lazy[c];
				lazy[c] = 0;
			}
			if (l > r || x > y || l > y || x > r)
				return;
			if (x <= l && y >= r)

			{
				lazy[c] += val;
				return;
			}
			int mid = l + r >> 1;
			update(l, mid, 2 * c + 1, x, y, val);
			update(mid + 1, r, 2 * c + 2, x, y, val);
			arr[c] = Math.max(arr[2 * c + 1], arr[2 * c + 2]);
		}

		int an(int ind) {
			return ans(0, n - 1, 0, ind);
		}

		int ans(int l, int r, int c, int ind) {
			if (lazy[c] != 0) {
				lazy[2 * c + 1] += lazy[c];
				lazy[2 * c + 2] += lazy[c];
				if (l == r)
					arr[c] += lazy[c];
				lazy[c] = 0;
			}
			if (l == r)
				return arr[c];
			int mid = l + r >> 1;
			if (mid >= ind)
				return ans(l, mid, 2 * c + 1, ind);
			return ans(mid + 1, r, 2 * c + 2, ind);
		}
	}

	public static int[] shuffle(int[] a, Random gen)
	{
		for (int i = 0, n = a.length; i < n; i++) {
			int ind = gen.nextInt(n - i) + i;
			int d = a[i];
			a[i] = a[ind];
			a[ind] = d;
		}
		return a;
	}

	long power(long x, long y, int mod)
	{
		long ans = 1;
		while (y > 0) {
			if (y % 2 == 0) {
				x = (x * x) % mod;
				y /= 2;
			} else {
				ans = (x * ans) % mod;
				y--;
			}
		}
		return ans;
	}

	// To Get Input
	// Some Buffer Methods
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;

	private int readByte() 
	{
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}

	private boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	private double nd() {
		return Double.parseDouble(ns());
	}

	private char nc() {
		return (char) skip();
	}

	private String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
									// ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	private int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

	private void tr(Object... o) {
		if (!oj)
			System.out.println(Arrays.deepToString(o));
	}
}