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 codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int k=sc.nextInt();
		int min=0;
		int k1=(int)(Math.log(n)/Math.log(2));
		int k2=(int)Math.pow(2,k1);
		int n1=n;
	
		PriorityQueue<Integer> pq=new PriorityQueue<Integer>(k,Collections.reverseOrder());
		while(n1!=0&&k2!=0){
		    int x=n1/k2;
		    min+=x;
		    for(int i=0;i<x;i++)
		        pq.add(k2);
		    n1=n1-x*k2;
		    k2=k2/2;
	       // System.out.println(n1+"----"+k2);
		}
	//	System.out.println(pq);
		if(k<min||k>n){
		    System.out.println("NO");
		    return ;
		}
		int st=pq.size();
		while(st!=k){
		    int val=pq.poll();
		    pq.offer(val/2);
		    pq.offer(val/2);
		    st++;
		}
		System.out.println("YES");
		for(int i=0;i<k;i++)
		    System.out.print(pq.poll()+" ");
		System.out.println();
		
	}
}