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 C5299 {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int k = scan.nextInt();
		ArrayList<Integer> arr = new ArrayList<>();
		for (int i = 0; i < 31; ++i) {
			if ((n & (1 << i)) > 0) {
				arr.add(1 << i);
			}
		}
		if(arr.size()>k){
			System.out.println("NO");
			return;
		}
		boolean good = false;
		for(int i = 0;i<arr.size();i++){
			if(arr.size()==k){
				good =true;
				break;
			}
			if(arr.get(i)!=1){
				arr.add(i, arr.get(i)/2);
				arr.add(i, arr.get(i+1)/2);
				arr.remove(i+2);
				i--;
			}
			
		}
		if(!good){
			System.out.println("NO");
			return;
		}
		System.out.println("YES");
		for(Integer curr:arr){
			System.out.print(curr+" ");
		}
	}

}