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.lang.*;
import java.awt.*;
import java.awt.geom.*;
import java.math.*;
import java.text.*;
import java.math.BigInteger.*;
import java.util.Arrays; 

public class   Sick
{
  BufferedReader in;
  StringTokenizer as;
  int nums[],nums2[];
  ArrayList < Integer > [] ar;
  
  public static void main (String[] args)
  {
    new Sick  ();
  }
  
  
  public int GCD(int a, int b) {
    if (b==0) return a;
    return GCD(b,a%b);
  }
  
  public Sick  ()
  {
    try
    {
      
      in = new BufferedReader (new InputStreamReader (System.in));
      int a = nextInt();
      int aa =a;
      int b = nextInt();
      nums = new int [400000];
      int counter = 0;
      for(int x = 0;x<aa;x++)
      {
        if(a == 0)
          break;
        if(a % 2 == 1)
        {
          nums[counter] = (int)(Math.pow(2,x));
          counter++;
        }
        a = a/2;
      }

      if(counter >b || b > aa)
        System.out.println("NO");
      else
      {
        int counter1 = 0;
        while(counter != b)
        {
          while(nums[counter1] == 1)
            counter1++;
          nums[counter1] = nums[counter1]/2;
          nums[counter] = nums[counter1];
          counter++;
        }
        System.out.println("YES");
        for(int x = 0;x < counter;x++)
        {
          System.out.print(nums[x] + " " );
        }
      }
    }
    
    catch(IOException e)
    {
      
    }
  }
  
  
  
  
  
  
  
  String next () throws IOException
  {
    while (as == null || !as.hasMoreTokens ())
    {
      as = new StringTokenizer (in.readLine ().trim ());
    }
    
    
    return as.nextToken ();
  }
  
  
  
  long nextLong () throws IOException
  {
    return Long.parseLong (next ());
  }
  
  
  int nextInt () throws IOException
  {
    return Integer.parseInt (next ());
  }
  
  
  double nextDouble () throws IOException
  {
    return Double.parseDouble (next ());
  }
  
  
  String nextLine () throws IOException
  {
    return in.readLine ().trim ();
  }
}