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 C1095{
	static int pro(int n,int k){
		int p=(int)(Math.log(n)/Math.log(2));
		p=(int)Math.pow(2,p);
		while(n-p<k){
			p/=2;
		}
		return p;
	}
	public static void main(String args[])throws IOException{
		Scanner sc=new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		PrintWriter pw=new PrintWriter(System.out);
		int n=sc.nextInt();
		int k=sc.nextInt();
		if(k>n){
			pw.println("NO");
		}
		else{
			pw.println("YES");
			while(n>0){
				k--;
				int p=pro(n,k);
				n-=p;
				if(k==0&&n!=0){
					System.out.println("NO");
					return;
				}
				pw.print(p+" ");
			}
		}
		pw.close();
	}
}