Problem: A positive integer x is called a power of two if it can be represented as x = 2^y, where y is a non-negative integer. So, the powers of two are 1, 2, 4, 8, 16, ....

You are given two positive integers n and k. Your task is to represent n as the sum of exactly k powers of two.

Input

The only line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 2 ⋅ 10^5).

Output

If it is impossible to represent n as the sum of k powers of two, print NO.

Otherwise, print YES, and then print k positive integers b_1, b_2, ..., b_k such that each of b_i is a power of two, and ∑ _{i = 1}^{k} b_i = n. If there are multiple answers, you may print any of them.

Examples

Input


9 4


Output


YES
1 2 2 4 


Input


8 1


Output


YES
8 


Input


5 1


Output


NO


Input


3 7


Output


NO

Solution (in JAVA):

Solution:

import java.util.*;
import java.io.*;
public class Main {
    public static void main(String[] args) throws IOException {
        //Code starts
        FastReader ip = new FastReader();
        OutputStream output = System.out;
        PrintWriter out = new PrintWriter(output);
        int n=ip.nextInt();
        int k=ip.nextInt();
        String s=Integer.toBinaryString(n);
        int v=0;
        Queue<Integer> q=new LinkedList<>();
        for(int i=s.length()-1;i>=0;i--){
            if(s.charAt(i)=='1'){
                q.add((int)Math.pow(2,v));
            }
            v++;
        }
       if(k<q.size()){
           out.println("NO");
       }else{
           int count=q.size();
           while(count!=k && !q.isEmpty()){
               int val=q.poll();
               if(val!=1){
                   q.add(val/2);
                   q.add(val/2);
                   count++;
               }
           }
           if(count<k){
               out.println("NO");
           }else{
               out.println("YES");
               if(q.size()<k){
                   while(q.size()!=k){
                       q.add(1);
                   }
               }
               for(Integer x:q){
                   out.print(x+" ");
               }

           }
       }


        out.close();
        //Code ends
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        FastReader() { br = new BufferedReader(new InputStreamReader(System.in)); }
        String next() { while (st == null || !st.hasMoreElements()) {
            try { st = new StringTokenizer(br.readLine()); }
            catch (IOException e) { e.printStackTrace(); } }
            return st.nextToken();
        }

        int nextInt() { return Integer.parseInt(next()); }
        long nextLong() { return Long.parseLong(next()); }
        double nextDouble() { return Double.parseDouble(next()); }

        String nextLine() {
            String str = "";
            try { str = br.readLine(); }
            catch (IOException e) { e.printStackTrace(); }
            return str;
        }
    }

}