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

public class Main
{
    public static void main(String[]args)
    {

        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);

        Solver solver = new Solver();
        solver.solve(1,in,out);
        out.close();
    }
    static class Solver
    {

        public int a[];

        public void solve(int ca,InputReader in,PrintWriter out)
        {
            int base = 1;
            int a[] = new int[40];
            a[0] = 1;
            for(int i = 1;i<31;i++)
            {
                base = base<<1;
                a[i] = base;
            }
            while(ca -- != 0)
            {
               int n = in.nextInt();
               int k = in.nextInt();
               if(n < k)
               {
                   out.print("NO");
               }
               else
               {
                   Vector<Integer> ans = new Vector<>();
                   for(int i = 30;i >=0;i--)
                   {
                       while(n >= 0 && a[i] <= n)
                       {
                            n -= a[i];
                            ans.add(a[i]);
                       }
                   }
                   if(ans.size() > k)
                   {
                       out.print("NO");
                   }
                   else
                   {
                       out.print("YES\n");
                       int p = 0,sz = ans.size();
                       while(sz < k)
                       {
                           int num = ans.elementAt(p);
                           if(num <= 1)
                           {
                               p++;
                               continue;
                           }
                           ans.setElementAt(num/2,p);
                           ans.add(num/2);
                           sz += 1;
                       }
                       for(int x : ans)
                       {
                           out.print(x+" ");
                       }
                   }
               }
            }
        }
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
        public BigInteger nextBigInteger()
        {
            return new BigInteger(next());
        }

    }
}