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.Scanner;
 
public class Main {
   public static void main(String[] args) {
	   Scanner scan=new Scanner(System.in);
	   int n=scan.nextInt();
	   int k=scan.nextInt();
	   int sum_1=0,num=0;
	   int bit[]=new int[50];
	   
	   while(n!=0){
		   bit[++num]=n&1;
		   n/=2;
		   if(bit[num]==1) 
			   sum_1++;
	   }
	  
	   while(sum_1<k){
		   if(num==1)
			   break;
		   bit[num]-=1;
		   bit[num-1]+=2;
		   if(bit[num]==0)
			   num-=1;
		   sum_1++;
	   }
	  
	   if(sum_1!=k){
		   System.out.println("NO");
	   }
	   else{
		   
		   int c=1;
		   System.out.println("YES");
		   for(int i=1;i<num;i++,c*=2){
			   for(int j=0;j<bit[i];j++){
				   System.out.print(c+" ");
			   }
		   }
		   for(int i=1;i<bit[num];i++){
			   System.out.print(c+" ");
		   }
		   System.out.println(c);
	   }
}
}