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.*;
import java.lang.*;
public class n_as_k_power_2 {

	public static void main(String[] args)throws IOException {
		BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
		String e = input.readLine();
		String arr[] = new String[2];
		arr = e.split(" ");
		int k= Integer.parseInt(arr[1]);
		long n= Long.parseLong(arr[0]);
		ArrayList<Integer> arr1 = new ArrayList<Integer>(Collections.nCopies(k, 1));
		int sum = k;
		for(int i=k-1;i>=0;--i) {
			while(sum+arr1.get(i)<=n) {
				sum+=arr1.get(i);
//				System.out.println(sum);
				int r = arr1.get(i);
				arr1.set(i, 2*r);
//				System.out.println(arr1);
			}
		}
//		System.out.println(sum);
//		System.out.println(arr1);
		if(sum == n) {
			System.out.println("YES");
			for(int g=0;g<arr1.size();g++) {
				System.out.print(arr1.get(g)+" ");
				
			}
		}
		else {
			System.out.println("NO");
		}
	
	}

}