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.*;

public class Testation {

	static int n;
	static int k;

	public static void main(String[] args) throws NumberFormatException, IOException {
		Scanner console = new Scanner(System.in);
		n = console.nextInt();
		k = console.nextInt();
		solve();
	}

	public static void solve() {
		Queue<Integer> avail = new LinkedList<>();
		Queue<Integer> done = new LinkedList<>();
		for (int i = 0; i < 32; i++) {
			if ((n & (1 << i)) != 0) {
				avail.add(1 << i);
			}
		}
		if (k > n || avail.size()>k) {
			System.out.println("NO");
		} else {
			System.out.println("YES");
			int cur;
			while ((done.size() + avail.size()) < k) {
				cur = avail.remove();
				if (cur == 1) {
					done.add(cur);
				} else {
					avail.add(cur / 2);
					avail.add(cur / 2);
				}
			}
			List<Integer> ans = new ArrayList<>();
			while (!avail.isEmpty()) {
				ans.add(avail.remove());
			}
			while (!done.isEmpty()) {
				ans.add(done.remove());
			}
			Collections.sort(ans);
			for (int i : ans) {
				System.out.print(i + " ");
			}
		}
	}
}