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.util.Scanner;

public class template  
{
	public static void main(String args[]) throws Exception
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int k=sc.nextInt();
		int y=n;
		PriorityQueue<Integer> p=new PriorityQueue<>(Collections.reverseOrder());
		if(n%2!=0)
		{
			y--;
			p.add(1);
		}
		while(y!=0)
		{
			int d=(int)((Math.log(y))/Math.log(2));
			int x=(int)Math.pow(2, d);
			p.add(x);
			y=y-x;
		}
		if(p.size()>k||k>n)
		{
			System.out.println("NO");
		}
	  
		else
		{
			while(p.size()!=k)
			{
				int a=p.poll();
				p.add(a/2);
				p.add(a/2);
			}
			System.out.println("YES");
			
			//int arr[]=new int[p.size()];
			p.toArray();
			for(Integer i:p)
			System.out.print(i+" ");
		}
	}
}