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.*;
public class Main{
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int k=sc.nextInt();
		PriorityQueue<Integer> queue=new PriorityQueue<>(k,Collections.reverseOrder());
		int count=0;
		for(int i=0;i<30;i++){
			if(((n>>i)&1)>0){
				queue.add(i);
				count++;
		//		System.out.println("hii");
			}
		}
		if(k<count || n<k){
			System.out.println("NO");	
			return ;
		}
		//System.out.println(queue);
		while(queue.size()<k){			
			int x=queue.peek();
			if(x==0){
				System.out.println("NO");
				//break;
				//queue.add(x);
				return ;
			}
			queue.poll();
			queue.add(x-1);
			queue.add(x-1);
			count++;
		}

		if(count==k){
			System.out.println("YES");
			while(!queue.isEmpty()){
				System.out.print((1<<queue.poll())+" ");
			}
		}
		
	}
}