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.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Scanner;



public class Main{
		
	public static void main(String[] args){
	
		Scanner scanner = new Scanner(System.in);
		
		int n = scanner.nextInt();
		int k = scanner.nextInt();
		
		int b = Integer.bitCount(n);
		if(n < k || b > k) System.out.println("NO");
		else {
			
			PriorityQueue<Integer> pQueue = new PriorityQueue<>(new Comparator<Integer>(){

				@Override
				public int compare(Integer o1, Integer o2) {
					return o2 - o1;
				}
				
			});
			
			for(int i = 0; i < 30 ;++i) {
				if(((1 << i) & n) > 0) pQueue.add(1 << i); 
			}
			
			while(pQueue.size() < k) {
				int element = pQueue.poll();
				pQueue.add(element / 2);
				pQueue.add(element / 2);
			}
			StringBuilder stringBuilder = new StringBuilder();
			stringBuilder.append("YES\n");
			while(!pQueue.isEmpty()) {
				stringBuilder.append(pQueue.poll() + " ");
			}
			
			System.out.println(stringBuilder);
			
			
		
			
		}
 		
		
		
	}
	
}