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
{
    static ArrayList<Integer>res = new ArrayList<>();
    static int n=0;
    static int arr[][];
    static int MAX = (int)1e5+1;
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner input = new Scanner(System.in);
	     n = input.nextInt();
		 int k = input.nextInt();
		 int mx = n;
		 int min =-1;
		 int count =0;
		 int countt = 0;
		 if(k == n){
		     System.out.println("YES");
		     for(int i =0;i<n;i++){
		         System.out.print(1+" ");
		     }
		     return;
		 }
		 Stack<Integer>res = new Stack<>();
		 for(int i =0;i<31;i++){
		     if((n&(1<<i)) != 0){
		         count++;
		         res.push((1<<i));
		     }
		 }
		 min = count;
		 countt = res.size();
		 int ans[] = new int[MAX];
		 if(k>=min && k<=mx){
		     System.out.println("YES");
		     int ptr = countt-1;
		     while(countt!=k && !res.isEmpty()){
		         int val = res.pop();
		         if(val/2 !=0){
		             res.push(val/2);
		             res.push(val/2);
		             countt++;
		         }else{
		             System.out.print(val+" ");
		         }
		     }
		     for(int val:res)System.out.print(val+" ");
		 }else{
		     System.out.println("NO");
		 }
		
	}
	public static void solve(int l,int r){
	    res.clear();
	    int next =-1;
	      for(int i =0;i<n;i++){
	          if(arr[l][0] == r){
	              next = arr[l][1];
	          }else if(arr[l][1] == r){
	              next = arr[l][0];
	          }else{
	              return;
	          }
	          l = r;
	          r = next;
	          res.add(next+1);
	      } 
	}
}