Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:

Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one. 

To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.

For definitions of powers and lexicographical order see notes.

Input

The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.

Output

Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.

It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].

Examples

Input

23 5


Output

Yes
3 3 2 1 0 


Input

13 2


Output

No


Input

1 2


Output

Yes
-1 -1 

Note

Sample 1:

23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23

Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.

Answers like (4, 1, 1, 1, 0) do not have the minimum y value.

Sample 2:

It can be shown there does not exist a sequence with length 2.

Sample 3:

<image>

Powers of 2:

If x > 0, then 2x = 2·2·2·...·2 (x times).

If x = 0, then 2x = 1.

If x < 0, then <image>.

Lexicographical order:

Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ.
/* 
 * UMANG PANCHAL
 * DAIICT
 */

import java.util.*;
import java.io.*;
import java.math.BigInteger;
import java.util.Comparator;
public class Main
{
 
	private static final Comparator<? super Integer> Comparator = null;
	static LinkedList<Integer> adj[];
	static ArrayList<Integer> adj1[];
	static int[] color,visited1;
	static boolean b[],visited[],possible;
	static int level[];
	static Map<Integer,HashSet<Integer>> s;
	static int totalnodes,colored;
	static int count[];
	static long sum[];
	static int nodes;
	static long ans=0;
	static long[] as=new long[10001];
	static long c1=0,c2=0;
	static int[] a,d,k;
	static int max=100000000;
	static long MOD = 1000000007,sm=0,m=Long.MIN_VALUE;
	static boolean[] prime=new boolean[1000005];
	static int[] levl;
    static int[] eat;
    static int price[];
    static int res[],par[];
    static int result=0;
    static int[] root,size;
    static boolean yes = true;
    static long p=Long.MAX_VALUE;
    static int start,end;
	// --------------------My Code Starts Here----------------------
	
	public static void main(String[] args) throws IOException
	{
		in=new InputReader(System.in);
		w=new PrintWriter(System.out);
     
		
		long n=nl();
	      int k=ni();
	      String s=Long.toBinaryString(n);
	     // w.println(s);
	      int no=0;
	      for(int i=0;i<s.length();i++)
	    	  if(s.charAt(i)=='1')
	    		  no++;
	      
	      if(k==no)
	      {
	    	  w.println("Yes");
	    	 for(int i=0;i<s.length();i++)
	    	 {
	    		 if(s.charAt(i)=='1')
	    			 w.print(s.length()-i-1+" ");
	    	 }
	      }
	      else if(k>no)
	      {
	    	  w.println("Yes");
	    	  PriorityQueue<Integer> pq = new PriorityQueue<Integer>(new Comparator<Integer>()
	    	  			{
	    	  				public int compare(Integer o1, Integer o2)
	    	  				{
	    	  					return Integer.compare(o2,o1);
	    	  				}
	    	  			});
	    	  for(int i=s.length()-1;i>=0;i--)
	     	 {
	     		 if(s.charAt(i)=='1')
	     			 pq.add(s.length()-1-i);
	     	 }
	    	  
	    	 while(pq.size()!=k)
	    	 {
	    		int x=pq.poll();
	    		x--;
	    		pq.add(x);
	    		pq.add(x);
	    	 }
	    
	    	 int max=pq.peek();
	    	 PriorityQueue<Integer> mpq = new PriorityQueue<Integer>();
	    	 while(!pq.isEmpty())
	    	    mpq.add(pq.poll());
	    	 PriorityQueue<Integer> mpq1 = new PriorityQueue<Integer>();
	    	 while(!mpq.isEmpty())
	    	 {
	    		 int x=mpq.poll();
	    		 if(x!=max && x==mpq.peek())
	    		 {
	    			 mpq.poll();
	    			 x++;
	    			 mpq1.add(x);
	    		 }
	    		 else
	    			 mpq1.add(x);
	    	 }
	    	 
	    	 while(mpq1.size()!=k)
	    	 {
	    		 int x=mpq1.poll();
		    		x--;
		    		mpq1.add(x);
		    		mpq1.add(x);
	    	 }
	    	 while(!mpq1.isEmpty())
	    		 pq.add(mpq1.poll());
	    	
	    	 while(!pq.isEmpty())
	    	  w.print(pq.poll()+" ");
	      }
	      else
	      {
	    	  w.print("No");
	      }
    	
    	   w.close();
    }


	


	// --------------------My Code Ends Here------------------------
     
	
	/*
	 *  PriorityQueue<Integer> pq = new PriorityQueue<Integer>(new Comparator<Integer>()
  			{
  				public int compare(Integer o1, Integer o2)
  				{
  					return Integer.compare(o2,o1);
  				}
  			});
	 * 
	 * 
	 */
	
	 public static void buildgraph(int n)
	 {
         adj=new LinkedList[n];
         visited=new boolean[n];
         level=new int[n];
         par=new int[n];
         for(int i=0;i<n;i++)
         	{
        	 adj[i]=new LinkedList<Integer>();
         	
         	}
      
	 }
	
	/*public static long kruskal(Pair[] p)
	{
		long ans=0;
		int w=0,x=0,y=0;
		for(int i=0;i<p.length;i++)
		{
			w=p[i].w;
			x=p[i].x;
			y=p[i].y;
			if(root(x)!=root(y))
			{
				ans+=w;
				union(x,y);
			}
		}
		return ans;
	}*/
	
	 static class Pair implements Comparable<Pair>
	 {
		Integer x;
		Long sum;
	
		Pair(int x,long sum)
		{
			this.x=x;
			this.sum=sum;
		}
		public int compareTo(Pair o)
		{
		  return (int)(sum-o.sum);
		  
		} 
		
	}
	
	public static int root(int i)
	{
		while(root[i]!=i)
		{
			root[i]=root[root[i]];
			i=root[i];
		}
		return i;
	}
	
	public static void init(int n)
	{
		root=new int[n+1];
		for(int i=1;i<=n;i++)
			root[i]=i;
	}
	public static void union(int a,int b)
	{
	    int root_a=root(a);	
	    int root_b=root(b);
	    root[root_a]=root_b;
	   // size[root_b]+=size[root_a];
	}


	
	public static boolean isPrime(int n)
	{
	    // Corner cases
	    if (n <= 1)  return false;
	    if (n <= 3)  return true;
	 
	    // This is checked so that we can skip 
	    // middle five numbers in below loop
	    if (n%2 == 0 || n%3 == 0)
	    	return false;
	 
	    for (int i=5; i*i<=n; i=i+6)
	        if (n%i == 0 || n%(i+2) == 0)
	           return false;
	 
	    return true;
	}
	

	
	public static String ns()
	{
		return in.nextLine();
	}
	public static int ni()
	{
		return in.nextInt();
	}
	public static long nl()
	{
		return in.nextLong();
	}
	public static int[] na(int n)
	{
		a=new int[n];
		for(int i=0;i<n;i++)
		a[i]=ni();
		return a;
	}
	public static void sieve()
	    {
	       int n=prime.length;
	        for(int i=0;i<n;i++)
	            prime[i] = true;
	         
	        for(int p = 2; p*p <=n; p++)
	        {
	            if(prime[p] == true)
	            {
	                for(int i = p*2; i <n; i += p)
	                    prime[i] = false;
	            }
	        }
	    }

  public static String rev(String s)
	{
		StringBuilder sb=new StringBuilder(s);
		sb.reverse();
		return sb.toString();
	}
	static long lcm(long a, long b)
	{
	    return a * (b / gcd(a, b));
	}
	static long gcd(long a, long b)
	{
	    while (b > 0)
	    {
	        long temp = b;
	        b = a % b; // % is remainder
	        a = temp;
	    }
	    return a;
	}
	static InputReader in;
	static PrintWriter w;
static class InputReader 
{
 
private final InputStream stream;
private final byte[] buf = new byte[8192];
private int curChar, snumChars;
private SpaceCharFilter filter;
 
public InputReader(InputStream stream)
{
  this.stream = stream;
}
 
public int snext()
{
  if (snumChars == -1)
    throw new InputMismatchException();
  if (curChar >= snumChars)
  {
    curChar = 0;
    try 
    {
      snumChars = stream.read(buf);
    }
    catch (IOException e)
    {
      throw new InputMismatchException();
    }
    if (snumChars <= 0)
      return -1;
  }
  return buf[curChar++];
}
 
public int nextInt() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  int sgn = 1;
  if (c == '-')
  {
    sgn = -1;
    c = snext();
  }
  int res = 0;
  do
  {
    if (c < '0' || c > '9')
      throw new InputMismatchException();
    res *= 10;
    res += c - '0';
    c = snext();
  }
  while (!isSpaceChar(c));
  return res * sgn;
}
 
public long nextLong() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  int sgn = 1;
  if (c == '-')
  {
    sgn = -1;
    c = snext();
  }
  long res = 0;
  do
  {
    if (c < '0' || c > '9')
      throw new InputMismatchException();
    res *= 10;
    res += c - '0';
    c = snext();
  }
  while (!isSpaceChar(c));
  return res * sgn;
}	    
public String readString() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  StringBuilder res = new StringBuilder();
  do
  {
    res.appendCodePoint(c);
    c = snext();
  }
  while (!isSpaceChar(c));
  return res.toString();
}
 
public String nextLine() 
{
  int c = snext();
  while (isSpaceChar(c))
    c = snext();
  StringBuilder res = new StringBuilder();
  do
  {
    res.appendCodePoint(c);
    c = snext();
  }
  while (!isEndOfLine(c));
  return res.toString();
}
 
public boolean isSpaceChar(int c)
{
  if (filter != null)
    return filter.isSpaceChar(c);
  return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
}
 
private boolean isEndOfLine(int c) 
{
  return c == '\n' || c == '\r' || c == -1;
}
 
public interface SpaceCharFilter
{
  public boolean isSpaceChar(int ch);
}
}
	
}