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.*;

public class b {
	public static void main(String[] args) throws IOException {
		Scanner zizo = new Scanner(System.in);
		PrintWriter wr = new PrintWriter(System.out);
		
		
		int n = zizo.nextInt();
		int t = n;
		int k = zizo.nextInt();
		ArrayList<Long>a = new ArrayList<>();
		for(int i = 30;i >=0;i--) {
			if(Math.pow(2, i) <= n) {
				n-=Math.pow(2, i);
				a.add(i*1l);
			}
		}//System.out.println(a);
		//System.out.println(a.size()+" "+ k+" "+n);
		if(a.size() > k || k > t) {
			System.out.println("NO");
			return;
		}
		k -= a.size();
		int i = 0;
		//System.out.println(a);
		while(k != 0) {
			long x = 0;
			if(a.get(i) == 0) {
				i++;
				continue;
			}
			long idx = 0;
			for(int j = 0;j <= a.get(i);j++) {
				if(Math.pow(2,a.get(i)-j)-1 <= k) {
					x = (long)Math.pow(2,a.get(i)-j)-1;
					idx = j;
					break;
				}
			}
			k-=x;
			for(int j = 0;j < x+1; j++) {
				a.add(idx);
			}
			a.remove(i);
		}
		wr.println("YES");
		for(long x : a) {
			wr.print((long)Math.pow(2, x)+" ");
		}
		wr.close();
	}
}

class Scanner 
{
	StringTokenizer st;
	BufferedReader br;

	public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

	public String next() throws IOException 
	{
		while (st == null || !st.hasMoreTokens()) 
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}

	public int nextInt() throws IOException {return Integer.parseInt(next());}

	public long nextLong() throws IOException {return Long.parseLong(next());}

	public String nextLine() throws IOException {return br.readLine();}

	public double nextDouble() throws IOException
	{
		String x = next();
		StringBuilder sb = new StringBuilder("0");
		double res = 0, f = 1;
		boolean dec = false, neg = false;
		int start = 0;
		if(x.charAt(0) == '-')
		{
			neg = true;
			start++;
		}
		for(int i = start; i < x.length(); i++)
			if(x.charAt(i) == '.')
			{
				res = Long.parseLong(sb.toString());
				sb = new StringBuilder("0");
				dec = true;
			}
			else
			{
				sb.append(x.charAt(i));
				if(dec)
					f *= 10;
			}
		res += Long.parseLong(sb.toString()) / f;
		return res * (neg?-1:1);
	}

	public boolean ready() throws IOException {return br.ready();}
}