Problem: This is the easy version of the problem. The difference between versions is the constraints on n and a_i. You can make hacks only if all versions of the problem are solved.

First, Aoi came up with the following idea for the competitive programming problem:

Yuzu is a girl who collecting candies. Originally, she has x candies. There are also n enemies numbered with integers from 1 to n. Enemy i has a_i candies.

Yuzu is going to determine a permutation P. A permutation is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, \{2,3,1,5,4\} is a permutation, but \{1,2,2\} is not a permutation (2 appears twice in the array) and \{1,3,4\} is also not a permutation (because n=3 but there is the number 4 in the array).

After that, she will do n duels with the enemies with the following rules:

  * If Yuzu has equal or more number of candies than enemy P_i, she wins the duel and gets 1 candy. Otherwise, she loses the duel and gets nothing. 
  * The candy which Yuzu gets will be used in the next duels. 



Yuzu wants to win all duels. How many valid permutations P exist?

This problem was easy and wasn't interesting for Akari, who is a friend of Aoi. And Akari made the following problem from the above idea:

Let's define f(x) as the number of valid permutations for the integer x.

You are given n, a and a prime number p ≤ n. Let's call a positive integer x good, if the value f(x) is not divisible by p. Find all good integers x.

Your task is to solve this problem made by Akari.

Input

The first line contains two integers n, p (2 ≤ p ≤ n ≤ 2000). It is guaranteed, that the number p is prime (it has exactly two divisors 1 and p).

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 2000).

Output

In the first line, print the number of good integers x.

In the second line, output all good integers x in the ascending order.

It is guaranteed that the number of good integers x does not exceed 10^5.

Examples

Input


3 2
3 4 5


Output


1
3


Input


4 3
2 3 5 6


Output


2
3 4


Input


4 3
9 1 1 1


Output


0

Note

In the first test, p=2.

  * If x ≤ 2, there are no valid permutations for Yuzu. So f(x)=0 for all x ≤ 2. The number 0 is divisible by 2, so all integers x ≤ 2 are not good. 
  * If x = 3, \{1,2,3\} is the only valid permutation for Yuzu. So f(3)=1, so the number 3 is good. 
  * If x = 4, \{1,2,3\} , \{1,3,2\} , \{2,1,3\} , \{2,3,1\} are all valid permutations for Yuzu. So f(4)=4, so the number 4 is not good. 
  * If x ≥ 5, all 6 permutations are valid for Yuzu. So f(x)=6 for all x ≥ 5, so all integers x ≥ 5 are not good. 



So, the only good number is 3.

In the third test, for all positive integers x the value f(x) is divisible by p = 3.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;


public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        Solve solver = new Solve();
        solver.solve(in, out);
        out.close();
    }
    
    static class Solve {
    	public void solve(InputReader in, OutputWriter out) {
    		int n,p;
    		n = in.nextInt();
    		p = in.nextInt();
    		int[] a = in.nextIntArray(n);
    		ArrayList<Integer> ans = new ArrayList<Integer>();
    		Arrays.sort(a);
    		for(int x = 1;x<=2000;x++) {
    			long prod = 1;
    			for(int i = 0;i<n;i++) {
    				int key = x+i;
    				
    				int low = 0;
    				int high = a.length - 1;
    				while(low <= high) {
    					int mid = (low + high) / 2;
    					if(a[mid] <= key) {
    						low = mid + 1;
    					}
    					else {
    						high = mid - 1;
    					}
    				}
    				int howMany = high - i + 1;
    				prod *= howMany % p;
    				prod %= p;
    				if(prod==0) {
    					break;
    				}
    			}if(prod % p !=0) {
    				ans.add(x);
				}
    		}System.out.println(ans.size());
    		for(int i = 0;i<ans.size();i++)System.out.print(ans.get(i)+" ");
    		System.out.println("");
    	}
    }
    
    static class Graph {
        int N;
        HashMap<Integer, LinkedList<Integer>> adyacentList;
        public Graph(int N) {
            this.N = N;
            adyacentList = new HashMap<>();
            for (Integer i = 1; i <= N; i++) {
                adyacentList.put(i, new LinkedList<Integer>());
            }
        }
        void addEdge(int node, int v) {
            this.adyacentList.get(node).add(v);
            this.adyacentList.get(v).add(node);
        }
        void bfs(int x, boolean[] visited) {
            LinkedList<Integer> queue = new LinkedList<>();
            queue.add(x);
            visited[x] = true;
            while (!queue.isEmpty()) {
                LinkedList<Integer> list = this.adyacentList.get(queue.poll());
                for (Integer n : list) {
                    if (!visited[n]) {
                        visited[n] = true;
                        queue.add(n);
                    }
                }
            }
        }
        void dfs(int x, boolean[] visited) {
            visited[x] = true;
            LinkedList<Integer> list = this.adyacentList.get(x);
            for (Integer n : list) {
                if (!visited[n]) {
                    visited[n] = true;
                    dfs(n, visited);
                }
            }
        }
    }
    
    static class OutputWriter {
	    private final PrintWriter writer;
	
	    public OutputWriter(OutputStream outputStream) {
	        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	    }
	
	    public OutputWriter(Writer writer) {
	        this.writer = new PrintWriter(writer);
	    }
	
	    public void close() {
	        writer.close();
	    }
	
	    public void println(String string) {
	        writer.println(string);
	    }
	    
	    public void println(int number) {
	        writer.println(number);
	    }
	    
	    public void println(long number) {
	        writer.println(number);
	    }
	    
	    public void print(long number) {
	        writer.print(number);
	    }
	    
	    public void print(int number) {
	        writer.print(number);
	    }
	    
	    public void print(String string) {
	        writer.print(string);
	    }
	}
    
	static class InputReader { 
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;
		
		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}
		
		public String nextLine() {
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (b!=10) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
		
		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}
 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
 
		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}
 
		public boolean hasNext() {
			skip();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
		
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
 
		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}
 
		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}