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.BufferedReader;
import java.io.*;
import java.util.*;
import java.util.StringTokenizer;
import java.util.Vector;
import java.lang.*;
import java.lang.Exception.*;
import java.util.InputMismatchException;

public class p1095C{
	public static Print print=new Print();
	public static Scan scan=new Scan();
	
	public static boolean isPower(int x){
		if(x==2)return true;
		if(x%2==1)return false;
		else{
			return isPower(x/2);
		}
	}
	public static Queue<Integer> bin(int x) throws Exception{
		int count=0;
		Queue<Integer> pos=new LinkedList<>();
		while(x!=0){
			if(x%2==1){
				
				pos.add((int)Math.pow(2,count));
				
			}
			x=x/2;
			count++;
		}
		return pos;
	}
	public static void check(Queue<Integer> pos,int k,int n) throws Exception{
			int count=0;
			while(pos.size()<k){
				int temp=pos.poll();
				//print.println(temp);
				if(temp/2!=0){
					pos.add(temp/2);
					pos.add(temp/2);
					count++;
				}
				else{
					pos.add(temp);
					count++;
					
				}
				//print.println(pos.size());
			}
			if(pos.size()!=k){
				print.println("NO");
			}
			else{
				for(int i:pos){
					print.print(i+" ");
				}
			}
			
			
		
	}
	
	
	public static void solve(int n,int k) throws Exception{
		Queue<Integer> pos=bin(n);
		if(k<pos.size())print.println("NO");

		else{
			int s=0;
			for(int i:pos){
				s+=i;
			}
		if(k>s)print.println("NO");
		else {
		print.println("YES");
		check(pos,k,pos.size());	
		}
			
		}
		
		
		
		
	}
	
	
	public static void main(String[] args) throws Exception{
		int n;
		int k;
		n=scan.scanInt();
		k=scan.scanInt();
		solve(n,k);
		//System.out.println(isPower(256));
		
		
		
		print.close();
	}
}


































class Scan
{
    private byte[] buf=new byte[1024];
    private int index;
    private InputStream in;
    private int total;
    public Scan()
    {
        in=System.in;
    }
    public int scan()throws IOException
    {
        if(total<0)
        throw new InputMismatchException();
        if(index>=total)
        {
            index=0;
            total=in.read(buf);
            if(total<=0)
            return -1;
        }
        return buf[index++];
    }
    public int scanInt()throws IOException
    {
        int integer=0;
        int n=scan();
        while(isWhiteSpace(n))
        n=scan();
        int neg=1;
        if(n=='-')
        {
            neg=-1;
            n=scan();
        }
        while(!isWhiteSpace(n))
        {
            if(n>='0'&&n<='9')
            {
                integer*=10;
                integer+=n-'0';
                n=scan();
            }
            else throw new InputMismatchException();
        }
        return neg*integer;
    }
    public double scanDouble()throws IOException
    {
        double doub=0;
        int n=scan();
        while(isWhiteSpace(n))
        n=scan();
        int neg=1;
        if(n=='-')
        {
            neg=-1;
            n=scan();
        }
        while(!isWhiteSpace(n)&&n!='.')
        {
            if(n>='0'&&n<='9')
            {
                doub*=10;
                doub+=n-'0';
                n=scan();
            }
            else throw new InputMismatchException();
        }
        if(n=='.')
        {
            n=scan();
            double temp=1;
            while(!isWhiteSpace(n))
            {
                if(n>='0'&&n<='9')
                {
                    temp/=10;
                    doub+=(n-'0')*temp;
                    n=scan();
                }
                else throw new InputMismatchException();
            }
        }
        return doub*neg;
    }
    public String scanString()throws IOException
    {
        StringBuilder sb=new StringBuilder();
        int n=scan();
        while(isWhiteSpace(n))
        n=scan();
        while(!isWhiteSpace(n))
        {
            sb.append((char)n);
            n=scan();
        }
        return sb.toString();
    }
    private boolean isWhiteSpace(int n)
    {
        if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
        return true;
        return false;
    }
}
class Print
{
    private final BufferedWriter bw;
    public Print()
    {
        this.bw=new BufferedWriter(new OutputStreamWriter(System.out));
    }
    public void print(Object object)throws IOException
    {
        bw.append(""+object);
    }
    public void println(Object object)throws IOException
    {
        print(object);
        bw.append("\n");
    }
    public void close()throws IOException
    {
        bw.close();
    }
}