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.text.DateFormat;
import java.text.ParseException;
import java.text.SimpleDateFormat;
import java.util.*;

public class Main {

    static final int INF = Integer.MAX_VALUE;

    static void mergeSort(int[] a, int p, int r) {
        if (p < r) {
            int q = (p + r) / 2;
            mergeSort(a, p, q);
            mergeSort(a, q + 1, r);
            merge(a, p, q, r);
        }
    }

    static void merge(int[] a, int p, int q, int r) {
        int n1 = q - p + 1;
        int n2 = r - q;
        int[] L = new int[n1 + 1], R = new int[n2 + 1];
        // int[] L1 = new int[n1 + 1], R1 = new int[n2 + 1];

        for (int i = 0; i < n1; i++) {
            L[i] = a[p + i];
            //  L1[i] = b[p + i];

        }
        for (int i = 0; i < n2; i++) {
            R[i] = a[q + 1 + i];
            // R1[i] = b[q + 1 + i];

        }
        L[n1] = R[n2] = INF;
        // L1[n1] = R1[n2] = INF;

        for (int k = p, i = 0, j = 0; k <= r; k++) {
            if (L[i] <= R[j]) {

                a[k] = L[i++];
                //  b[k] = L1[i++];

            } else {
                a[k] = R[j++];
                // b[k] = R1[j++];

            }
        }
    }

    static void mergeSort(int[] a, long[] b, int[] c, int p, int r) {
        if (p < r) {
            int q = (p + r) / 2;
            mergeSort(a, b, c, p, q);
            mergeSort(a, b, c, q + 1, r);
            merge(a, b, c, p, q, r);
        }
    }

    static void merge(int[] a, long[] b, int[] c, int p, int q, int r) {
        int n1 = q - p + 1;
        int n2 = r - q;
        int[] L = new int[n1 + 1], R = new int[n2 + 1];
        long[] L1 = new long[n1 + 1], R1 = new long[n2 + 1];
        int[] L2 = new int[n1 + 1], R2 = new int[n2 + 1];
        // int[] L2 = new int[n1 + 1], R2 = new int[n2 + 1];

        for (int i = 0; i < n1; i++) {
            L[i] = a[p + i];
            L1[i] = b[p + i];
            L2[i] = c[p + i];
            // L2[i] = a[p + i];
        }
        for (int i = 0; i < n2; i++) {
            R[i] = a[q + 1 + i];
            R1[i] = b[q + 1 + i];
            R2[i] = c[q + 1 + i];
            //  R2[i] = a[q + 1 + i];
        }
        L[n1] = R[n2] = INF;
        L1[n1] = R1[n2] = INF;
        L2[n1] = R2[n2] = INF;

        for (int k = p, i = 0, j = 0; k <= r; k++) {
            if (L[i] <= R[j]) {
                a[k] = L[i];
                b[k] = L1[i];
                c[k] = L2[i++];
                // c[k] = L2[i++];
            } else {
                a[k] = R[j];
                b[k] = R1[j];
                c[k] = R2[j++];
            }
        }
    }

    public static int[] sieve(int n) {
        int a[] = new int[n + 1];
        for (int i = 2; i <= n; i++) {
            a[i] = 1;
        }
        for (int i = 2; i <= Math.sqrt(n); i++) {
            if (a[i] == 1) {
                for (int k = 2; i * k <= n; k++) {
                    a[i * k] = 0;
                }
            }
        }
        return a;
    }

    public static long sum(int a) {
        long su = 0;
        while (a > 0) {
            su += (long) a % 10;
            a /= 10;
        }
        return su;
    }

    public static int divi(int b) {
        int n = 0;
        for (int i = 2; i <= Math.sqrt(b); i++) {
            if (b % i == 0) {
                n = i;
                break;
            }
        }
        if (n == 0) {
            return b;
        }
        return n;
    }

    public static boolean prime(int n) {
        if (n == 1) {
            return true;
        }

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

    public static String reve(int a, int b, String s) {
        String q = "";
        for (int i = b; i >= a; i--) {
            q += s.charAt(i);
        }
        return q;
    }

    public static boolean isvowel(char c) {
        if (c == 'a' || c == 'e' || c == 'i' || c == 'o' || c == 'u' || c == 'y') {
            return true;
        } else {
            return false;
        }
    }

    static long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    public static int hole(int n) {
        int y = 0;
        if (n == 1) {
            return 0;
        }
        if (prime(n)) {
            return 1;
        }
        for (int i = 2; i <= Math.sqrt(n); i++) {
            if (n % i == 0) {
                if (prime(i)) {
                    y++;
                }
                if (prime(n / i) && i != (n / i)) {
                    y++;
                }
            }
        }
        return y;
    }

    static List<Integer> gd(int a, int b) {
        int m = (int) gcd(a, b);
        List<Integer> q = new ArrayList();
        for (int i = 1; i * i <= m; ++i) {
            if (m % i == 0) {
                q.add(i);
                if (i != m / i) {
                    q.add(m / i);
                }
            }
        }
        return q;
    }

    static boolean contain(int[] a) {
        for (int i = 1; i < a.length; i++) {
            if (a[i] == 0) {
                return true;
            }
        }
        return false;
    }

    static void decrease(int[] a) {
        for (int i = 1; i < a.length; i++) {
            a[i]--;
        }
    }

    static long power(StringBuilder s) {
        long c = 1, sum = 0;
        for (int i = 0; i < s.length(); i++) {
            if (s.charAt(i) == 'C') {
                c *= 2;
            } else {
                sum += c;
            }
        }
        return sum;
    }

    static long sum(long n) {
        return n * (n + 1) / 2;
    }

    static int divisors(int n) {
        Set<Integer> c = new HashSet();
        for (int i = 1; i <= Math.sqrt(n); i++) {
            if (n % i == 0) {
                c.add(i);
                c.add((int) (n / i));
            }
        }
        return c.size();
    }

    static boolean cal(int val, int k, int t) {
        int res = val, p = 1;
        while (val / Math.pow(k, p) > 0) {
            res += val / Math.pow(k, p);
            p++;
        }
        return res >= t;
    }

    static int Last_Ocuu(int[] a, int n, long v) {
        int start = 0, end = n - 1, mid, ans = -1;

        while (start <= end) {
            mid = (start + end) >> 1;
            if (a[mid] < v) {
                ans = mid;
                end = mid - 1;
            } else if (a[mid] >= v) {
                //ans=mid;
                start = mid + 1;
            }

        }
        return ans;
    }

    static void print(int a, String s) {

        if (a > 0) {
            //s+='*';
            System.out.println(s);
            print(a - 1, '*' + s);
        } else {
            return;
        }
    }

    static long max(int[] a) {

        long m = 0;
        int max = a[a.length - 1];
        for (int i = a.length - 1; i > 0; i--) {
            if (a[i] == a[i - 1]) {
                m++;
            }
        }
        if (m == 0) {
            m++;
        }
        return m;
    }

    static long summtion(int[] a) {
        long s = 0;
        for (int i = 1; i < a.length; i++) {
            s += (long) a[i];
        }
        return s;
    }

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

    static int min(int[] a, PriorityQueue<Integer> d, int n) {
        int b = 0;
        int va = a[0];
        for (int i = 0; i <= n; i++) {
            if (va > a[i] && a[i] != d.peek()) {
                va = a[i];
                b = i;
            }
        }
        return b;
    }

    public static void main(String[] args) throws IOException, ParseException {
        Scannerr in = new Scannerr(System.in);
        PrintWriter or = new PrintWriter(System.out);
        //Scanner w = new Scanner(System.in);
        //BitSet s= new BitSet();
      int n = in.nextInt(), m = in.nextInt();
      int[] a= new int[n];
      for(int i=0;i<n;i++)a[i]=in.nextInt();
        mergeSort(a, 0, n-1);
        ArrayList<Integer> li = new ArrayList();
        int p=1;
        for (int i = 0; i < n;p++ ) {
            if (m==0||m<p) break;
            if (a[i]==p) {
                i++;
            }
            else{
                if (m>=p&&p!=a[i]) {
                    li.add(p);
                    m-=p;
                }
            }
        }
        for (int i = p; true; i++) {
            if (m==0||m<i) break;
                    if (m>=i &&i!=a[n-1]) {
                    li.add(i);
                    m-=i;
                }
        }
      or.println(li.size());
      for(int y:li)or.print(y+" ");
        or.flush();
    }

    static class Scannerr {

        StringTokenizer st;
        BufferedReader br;

        public Scannerr(FileReader fileReader) throws FileNotFoundException {
            br = new BufferedReader(fileReader);
        }

        public Scannerr(InputStream s) throws FileNotFoundException {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
            }
            return st.nextToken();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++) {
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec) {
                        f *= 10;
                    }
                }
            }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

    }

}

class Pair {

    int ind;
    int val;
    //int min;
    public Pair(int n, int p) {
        ind = n;
        val = p;
        // min = m;
    }

}