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.*;
import java.util.*;

public class Main {

	static int mod = (int) 1e9 + 7;
	static int MAX = (int) 1e7;

	public static void main(String[] args) {
		FasterScanner s = new FasterScanner();
		PrintWriter out = new PrintWriter(System.out);
		int test = 1;
		testloop:
			while (test-- > 0) {
				int n=s.nextInt();
				int m=s.nextInt();
				int[] a = s.nextIntArray(n);
				Arrays.sort(a);
				int cur=1;
				int i=0;
				ArrayList<Integer> ans = new ArrayList<>();
				while(m>=cur){
					if(i<n && cur==a[i]){
						cur++;
						i++;
						continue;
					}
					else{
						m-=cur;
						ans.add(cur);
						cur++;
					}
				}
				out.println(ans.size());
				for(i=0;i<ans.size();i++){
					out.print(ans.get(i)+" ");
				}
			}
		out.close();
	}
	static class Player implements Comparable<Player>{
		String name;
		int score;
		Player(String n,int v){
			name = n;
			score = v;
		}
		@Override
		public int compareTo(Player o) {
			return o.score-score;
		}
	}
	static class Edge {
		int t, rev, f;
		long cap;

		public Edge(int t, int rev, long cap) {
			this.t = t;
			this.rev = rev;
			this.cap = cap;
		}
	}

	public static List<Edge>[] createGraph(int nodes) {
		List<Edge>[] graph = new List[nodes];
		for (int i = 0; i < nodes; i++)
			graph[i] = new ArrayList<>();
		return graph;
	}

	public static void addEdge(List<Edge>[] graph, int s, int t, long cap) {
		graph[s].add(new Edge(t, graph[t].size(), cap));
		graph[t].add(new Edge(s, graph[s].size() - 1, 0));
	}

	static boolean dinicBfs(List<Edge>[] graph, int src, int dest, int[] dist) {
		Arrays.fill(dist, -1);
		dist[src] = 0;
		int[] Q = new int[graph.length];
		int sizeQ = 0;
		Q[sizeQ++] = src;
		for (int i = 0; i < sizeQ; i++) {
			int u = Q[i];
			for (Edge e : graph[u]) {
				if (dist[e.t] < 0 && e.f < e.cap) {
					dist[e.t] = dist[u] + 1;
					Q[sizeQ++] = e.t;
				}
			}
		}
		return dist[dest] >= 0;
	}

	static long dinicDfs(List<Edge>[] graph, int[] ptr, int[] dist, int dest, int u, long l) {
		if (u == dest)
			return l;
		for (; ptr[u] < graph[u].size(); ++ptr[u]) {
			Edge e = graph[u].get(ptr[u]);
			if (dist[e.t] == dist[u] + 1 && e.f < e.cap) {
				long df = dinicDfs(graph, ptr, dist, dest, e.t, Math.min(l, e.cap - e.f));
				if (df > 0) {
					e.f += df;
					graph[e.t].get(e.rev).f -= df;
					return df;
				}
			}
		}
		return 0;
	}

	public static long maxFlow(List<Edge>[] graph, int src, int dest) {
		long flow = 0;
		int[] dist = new int[graph.length];
		while (dinicBfs(graph, src, dest, dist)) {
			int[] ptr = new int[graph.length];
			while (true) {
				long df = dinicDfs(graph, ptr, dist, dest, src, Integer.MAX_VALUE);
				if (df == 0)
					break;
				flow += df;
			}
		}
		return flow;
	}

	static int ans(ArrayList<Character>[] l, char a, int n) {
		if (n == 1)
			return 1;
		int sum = 0;
		for (int i = 0; i < l[a - 'a'].size(); i++) {
			sum += ans(l, l[a - 'a'].get(i), n - 1);
		}
		return sum;
	}

	static void dfs1(List<Integer>[] graph, boolean[] used, List<Integer> order, int u) {
		used[u] = true;
		for (int v : graph[u])
			if (!used[v])
				dfs1(graph, used, order, v);
		order.add(u);
	}

	static void dfs2(List<Integer>[] reverseGraph, int[] comp, int u, int color) {
		comp[u] = color;
		for (int v : reverseGraph[u])
			if (comp[v] == -1)
				dfs2(reverseGraph, comp, v, color);
	}

	public static boolean[] solve2Sat(List<Integer>[] graph) {
		int n = graph.length;
		boolean[] used = new boolean[n];
		List<Integer> order = new ArrayList<>();
		for (int i = 0; i < n; ++i)
			if (!used[i])
				dfs1(graph, used, order, i);

		List<Integer>[] reverseGraph = new List[n];
		for (int i = 0; i < n; i++)
			reverseGraph[i] = new ArrayList<>();
		for (int i = 0; i < n; i++)
			for (int j : graph[i])
				reverseGraph[j].add(i);

		int[] comp = new int[n];
		Arrays.fill(comp, -1);
		for (int i = 0, color = 0; i < n; ++i) {
			int u = order.get(n - i - 1);
			if (comp[u] == -1)
				dfs2(reverseGraph, comp, u, color++);
		}

		for (int i = 0; i < n; ++i)
			if (comp[i] == comp[i ^ 1])
				return null;

		boolean[] res = new boolean[n / 2];
		for (int i = 0; i < n; i += 2)
			res[i / 2] = comp[i] > comp[i ^ 1];
		return res;
	}

	public static int[] createSets(int size) {
		int[] p = new int[size];
		for (int i = 0; i < size; i++)
			p[i] = i;
		return p;
	}

	public static int root(int[] p, int x) {
		return x == p[x] ? x : (p[x] = root(p, p[x]));
	}

	public static void unite(int[] p, int a, int b) {
		a = root(p, a);
		b = root(p, b);
		if (a != b)
			p[a] = b;
	}

	public static boolean nextPermutation(int[] p) {
		for (int a = p.length - 2; a >= 0; --a)
			if (p[a] < p[a + 1])
				for (int b = p.length - 1;; --b)
					if (p[b] > p[a]) {
						int t = p[a];
						p[a] = p[b];
						p[b] = t;
						for (++a, b = p.length - 1; a < b; ++a, --b) {
							t = p[a];
							p[a] = p[b];
							p[b] = t;
						}
						return true;
					}
		return false;
	}

	public static boolean isPrime(long n) {
		if (n <= 1)
			return false;
		for (long i = 2; i * i <= n; i++)
			if (n % i == 0)
				return false;
		return true;
	}

	static class SegTree {
		long[] val;
		int n;

		SegTree(int n) {
			val = new long[2 * n];
			this.n = n;
		}

		void upd(int p,long l) {
			p += n;
			val[p] += l;
			for (; (p >>= 1) != 0;) {
				val[p] = val[2 * p] +  val[2 * p + 1];
				if(val[p]>mod)
					val[p]-=mod;
			}
		}

		long query(int l, int r) { // sum on interval [l, r)
			// System.out.println(l+" "+r);
			long res = 0;
			for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
				if ((l & 1) != 0)
					res = res + val[l++];
				if ((r & 1) != 0)
					res = res+ val[--r];
				if(res>mod)
					res-=mod;
			}
			return res;
		}
	}

	static boolean check(int i, int j, int n) {
		if (i >= 0 && j >= 0 && i < n && j < n)
			return true;
		return false;
	}

	public static int[] generateDivisorTable(int n) {
		int[] divisor = new int[n + 1];
		for (int i = 1; i <= n; i++)
			divisor[i] = i;
		for (int i = 2; i * i <= n; i++)
			if (divisor[i] == i)
				for (int j = i * i; j <= n; j += i)
					divisor[j] = i;
		return divisor;
	}

	public static int[][] matrixMul(int[][] a, int[][] b) {
		int n = a.length;
		int m = a[0].length;
		int k = b[0].length;
		int[][] res = new int[n][k];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < k; j++) {
				for (int p = 0; p < m; p++) {
					res[i][j] = (res[i][j] + (int) ((a[i][p] * 1l * b[p][j]) % mod)) % mod;
				}
			}
		}
		return res;
	}

	public static int[][] matrixPow(int[][] a, int p) {
		if (p == 0) {
			return matrixUnit(a.length);
		} else if (p % 2 == 0) {
			return matrixPow(matrixMul(a, a), p / 2);
		} else {
			return matrixMul(a, matrixPow(a, p - 1));
		}
	}

	public static int[][] matrixUnit(int n) {
		int[][] res = new int[n][n];
		for (int i = 0; i < n; ++i) {
			res[i][i] = 1;
		}
		return res;
	}

	static int[] modInv(int n, int mod) {
		int[] ans = new int[n];
		for (int i = 1; i < n; i++)
			ans[i] = (int) pow(i, mod - 2, mod);
		return ans;
	}

	static int[] primes;

	public static long ncr(int n, int r) {
		if (n < r)
			return 0;
		if (n == r)
			return 1;
		if (r == 0)
			return 1;
		if (r < 0)
			return 0;
		long ans = 1;
		for (int i = 0; i < primes.length; i++) {
			long power = count(n, primes[i]) - count(n - r, primes[i]) - count(r, primes[i]);
			ans *= pow(primes[i], power, mod);
			ans %= mod;
		}
		return ans;
	}

	public static long pow(long x, long n, int mod) {
		long res = 1;
		for (long p = x; n > 0; n >>= 1, p = (p * p) % mod) {
			if ((n & 1) != 0) {
				res = (int) (res * p % mod);
			}
		}
		return res;
	}

	public static long count(int n, int p) {
		long count = 0;
		long z = p;
		while (z <= n) {
			count += n / z;
			z *= p;
		}
		return count;

	}

	public static int[] generatePrimes(int n) {
		boolean[] prime = new boolean[n + 1];
		Arrays.fill(prime, 2, n + 1, true);
		for (int i = 2; i * i <= n; i++)
			if (prime[i])
				for (int j = i * i; j <= n; j += i)
					prime[j] = false;
		int[] primes = new int[n + 1];
		int cnt = 0;
		for (int i = 0; i < prime.length; i++)
			if (prime[i])
				primes[cnt++] = i;

		return Arrays.copyOf(primes, cnt);
	}

	static class Pairxy implements Comparable<Pairxy> {
		int x;
		int y;

		Pairxy(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public int compareTo(Pairxy o) {
			return Integer.compare(this.x, o.x);
		}

	}

	static class Pair implements Comparable<Pair> {
		long val;
		int ind;

		Pair(long v, int i) {
			val = v;
			ind = i;
		}

		public int compareTo(Pair o) {
			if (this.val != o.val)
				return Long.compare(this.val, o.val);
			return Integer.compare(this.ind, o.ind);
		}
	}

	public static long C(int n, int r) {
		long ans = 1;
		int x = 1;
		while (x <= r) {
			ans *= n;
			ans /= x;
			x++;
			n--;
		}
		return ans;
	}

	static class DisjointSetsRank {

		int[] p;
		int[] rank;

		public DisjointSetsRank(int size) {
			p = new int[size];
			for (int i = 0; i < size; i++)
				p[i] = i;
			rank = new int[size];
		}

		public int root(int x) {
			return x == p[x] ? x : (p[x] = root(p[x]));
		}

		public int sameSet(int x, int y) {
			if (root(x) == root(y))
				return 1;
			return 0;

		}

		public void unite(int a, int b) {
			a = root(a);
			b = root(b);
			if (a == b)
				return;

			if (rank[a] < rank[b]) {
				p[a] = b;
			} else {
				p[b] = a;
				if (rank[a] == rank[b])
					++rank[a];
			}
		}

	}

	static int gcd(long m, long n) {
		long x;
		long y;
		while (m % n != 0) {
			x = n;
			y = m % n;
			m = x;
			n = y;
		}
		return (int) n;
	}

	static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;

		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

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

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

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}
}