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:
//package sept;

import java.io.*;
import java.util.*;

public class TimePass implements Runnable {
    InputStream is;
    PrintWriter out;
    String INPUT = "1 2";
    //boolean codechef=false;
    boolean codechef=true;
    static int mod=998244353;
    static int mod2=1000000007;
	
    void solve() throws IOException
	{
    	int n=ni();
    	int k=ni();
    	int curr=n;
    	int ind=0;ArrayList<Integer> l=new ArrayList<>();
    	while(curr>0)
    	{
    		if(curr%2==1)
    		{
    			l.add(1<<ind);
    		}
    		curr/=2;
    		ind++;
    	}
    	if(k>n || k<l.size())
    	{
    		System.out.println("NO");
    		return;
    	}
    	if(k==n)
    	{
    		System.out.println("YES");
    		for(int i=0;i<k;i++)System.out.print(1+" ");
    		System.out.println();
    		return;
    	}
    	int diff=k-l.size();
    	int sum=0;
    	ArrayList<Integer> ans=new ArrayList<>();
    	for(int i=l.size()-1;i>=0;i--)
    	{
    		sum+=l.get(i)-1;
    		if(sum>=diff)
    		{
    			int sz=sum-(l.get(i)-1)+((i))+l.size()-(i+1);
    			for(int j=0;j<sz-i;j++)
    			{
    				ans.add(1);
    			}
    			for(int j=i-1;j>=0;j--)
    			{
    				//System.out.println(j);
    				ans.add(l.get(j));
    			}
    			int req=k-sz;
    			LinkedList<Integer> ll1=new LinkedList<>();
    			LinkedList<Integer> ll2=new LinkedList<>();
    			ll1.add(l.get(i));
    			while(ll1.size()+ll2.size()!=req)
    			{
    				if(ll1.isEmpty())break;
    				int top=ll1.removeLast();
    				if(top/2==1)
    				{
    					ll2.add(1);
    					ll2.add(1);
    				}
    				else
    				{
    					ll1.add(top/2);
        				ll1.add(top/2);
    				}	
    			}
    			ans.addAll(ll1);
    			ans.addAll(ll2);
    			break;
    		}
    	}
    	if(ans.size()!=k)
    	{
    		System.out.println("NO");
    		return;
    	}
    	System.out.println("YES");
    	//System.out.println(ans.size());
    	int sum2=0;
    	for(int i:ans)
    	{
    		sum2+=i;
    		System.out.print(i+" ");
    	}
    		
    	System.out.println();
    	//System.out.println(sum2);
	}
    
    static int[] sum;
    static int[] a;
    
    static void dfs(int u,int[][] g,int par)
    {
    	//System.out.println(u+"u:"+sum[u]);
    	int min=Integer.MAX_VALUE;
    	if(g[u].length==0)
    	{
    		if(sum[u]==-1)
    		{
    			sum[u]=0;
    			return;
    		}
    	}
    	for(int v:g[u])
    	{
    		min=Math.min(min, sum[v]);
    	}
    	if(sum[u]==-1 && par!=-1 && min!=-1)
    	{
    		sum[u]=min;
    		a[u]=min-sum[par];
    	}
    	for(int v:g[u])
    	{
    		if(sum[v]!=-1 && min!=-1)
    		a[v]=sum[v]-min;
    		dfs(v,g,u);
    		//min=Math.min(min, sum[v]);
    	}
    }

	static long fnc(int x,int y)
    {
    	return x+(long)1000000007*y;
    }

	static int[][] packD(int n,int[] from,int[] to)
	{
		int[][] g=new int[n][];
		int[] p=new int[n];
		for(int f:from)
		{
			p[f]++;
		}
		int m=from.length;
		for(int i=0;i<n;i++)
		{
			g[i]=new int[p[i]];
		}
		for(int i=0;i<m;i++)
		{
			g[from[i]][--p[from[i]]]=to[i];
		}
		return g;
	}
	    
    static class Pair
    {
        int a,b;
        public Pair(int a,int b)
        {
            this.a=a;
            this.b=b;
        }
    }
    
    static long lcm(int a,int b)
    {
        long val=a;
        val*=b;
        return (val/gcd(a,b));
    }
    
    static long gcd(long a,long b)
    {
        if(a==0)return b;
        return gcd(b%a,a);
    }
    
    static int pow(int a, int b, int p)
    {
        long ans = 1, base = a;
        while (b!=0)
        {
            if ((b & 1)!=0)
            {
                ans *= base;
                ans%= p;
            }
            base *= base;
            base%= p;
            b >>= 1;
        }
        return (int)ans;
    }

    static int inv(int x, int p)
    {
        return pow(x, p - 2, p);
    }
    
    public void run()
    {
        if(codechef)oj=true;
        is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        
        long s = System.currentTimeMillis();
        try {
			solve();
		} catch (IOException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
        out.flush();
        tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception {new Thread(null,new TimePass(),"Main",1<<26).start();}
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
    private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}