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 Solution {
	public static final String NL = "\n";
	public static final String SP = " ";
	public static final String YES = "YES";
	public static final String NO = "NO";
	public void append(StringBuffer sb, List<Integer> arr) {
		for (int val: arr) {
			sb.append(val);
			sb.append(" ");
		}
		sb.append(NL);
	}

	public void append(StringBuffer sb, int[] arr) {
		for (int val: arr) {
			sb.append(val);
			sb.append(" ");
		}
		sb.append(NL);
	}

	public void append(StringBuffer sb, String... strs) {
		for (String str: strs) {
			sb.append(str);
			sb.append(" ");
		}
		sb.append(NL);
	}

	public void run() throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
		StringBuffer sb = new StringBuffer();

		String[] split = br.readLine().split(SP);
		int n = Integer.parseInt(split[0]);
		int k = Integer.parseInt(split[1]);

		int nn = n;
		int kk = k;
		String res;
		Stack<Integer> stack = new Stack<>();
		if (k > n) {
			res = NO;
		} else {
			while (n > 0) {
				stack.push(n - (n & (n - 1)));
				n = n & (n - 1);
				k--;
			}

			if (k >= 0) {
				res = YES;
			} else {
				res = NO;
			}
		}

		append(sb, res);

		if (res.equals(YES)) {
			List<Integer> arr = new ArrayList<>();
			while (k > 0) {
				int val = stack.pop();
				if (val == 1) arr.add(val);
				else {
					stack.push(val >> 1);
					stack.push(val >> 1);
					k--;
				}
			}
			while (!stack.isEmpty()) {
				arr.add(stack.pop());
			}

			append(sb, arr);
		}
		
		bw.write(sb.toString());
		bw.flush();
		bw.close();
		br.close();
	}

	public static void main(String[] args) throws IOException {
		new Solution().run();
	}
}