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

public class Main
{
    static class Reader {
		BufferedReader br;
		StringTokenizer st;
 
		public Reader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(next());
		}
 
		long nextLong() {
			return Long.parseLong(next());
		}
 
		double nextDouble() {
			return Double.parseDouble(next());
		}
 
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
 
	}
	public static void main(String[] args) throws IOException 
	{
		Reader sc=new Reader();Main G=new Main();
		PrintWriter o = new PrintWriter(System.out);
		int n=sc.nextInt();int k=sc.nextInt();
		int c[]=new int[30],k1=29;int s=0;
		for (int i=0;i<30;i++)
		{
		    c[i]=(n/(int)Math.pow(2,i))%2;
		    if (c[i]==1) {s++;k1=i;}
		}
		//o.println(Arrays.toString(c));
		if (k>n || k<s)o.println("NO");
		else
		{
		    o.println("YES");
		    while (s<k)
		    {
		        if (c[k1]>0){s++;c[k1]--;c[k1-1]+=2;}
		        else k1--;
		        //o.println(Arrays.toString(c));
		    }
		    for (int i=0;i<30;i++)
		    {
		        for (int j=0;j<c[i];j++)
		        o.print((int)Math.pow(2,i)+" ");
		    }
		}
		
		
		
		//o.println(h1);
		//o.println(h2);
		//o.println(h3);
		
        o.flush();
        o.close();
	}
}