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 ProblemC {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);

		long n = scan.nextLong();
		long k = scan.nextLong();

		if (k > n) {
			System.out.println("NO");
			return;
		}
		PriorityQueue<Integer> pows = new PriorityQueue<>(Comparator.reverseOrder());
		long i = 1;
		while (i <= n) {
			if ((i & n) > 0) {
				pows.add((int) i);
			}
			i <<= 1;
		}

		if (pows.size() > k) {
			System.out.println("NO");
			return;
		}

		while (pows.size() < k) {
			int top = pows.remove();
			pows.add(top / 2);
			pows.add(top / 2);
		}

		StringBuilder res = new StringBuilder("YES");
		res.append("\n");

		for (int num : pows) {
			res.append(num).append(" ");
		}
		res.append("\n");
		System.out.println(res);
	}
}