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 temp = k;
		int[] arr = new int[k];
		for(int i = 0;i < k;i++){
			arr[i] = 1;
			while(temp+arr[i]<=n){
				
				temp+=arr[i];
				arr[i]*=2;
				
			}
			
			
		}
		
		if(temp!=n) System.out.println("NO");
		else{
			
			System.out.println("YES");
			for(int i = 0;i < k;i++){
				
				System.out.print(arr[i]+" ");
				
			}
			
		}
			
	}


}