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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Task solver = new Task();
		solver.solve(1, in, out);
		out.close();
	}

	static class Task {
		List<Integer> inds = new ArrayList<>();

		public void solve(int testNumber, InputReader in, PrintWriter out) {
			int n = in.nextInt();
			int k = in.nextInt();
			int[] pows = new int[30];
			pows[0] = 1;
			for (int i = 1; i < 30; i++) {
				pows[i] = pows[i - 1] * 2;
			}
			if (lookFor(pows, 29, n, k)) {
				out.println("YES");
				for (int i = 0; i < inds.size(); i++) {
					out.print(pows[inds.get(i)] + " ");
				}
				out.println();
			} else {
				out.println("NO");
			}
		}

		private boolean lookFor(int[] pows, int ind, int n, int k) {
			while (pows[ind] + (k - 1) > n) {
				ind--;
				if (ind < 0)
					return false;
			}
			inds.add(ind);
			n -= pows[ind];
			k--;
			if (n == 0 && k == 0)
				return true;
			else if (n > 0 && k > 0)
				return lookFor(pows, ind, n, k);
			else
				return false;
		}
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public Long nextLong() {
			return Long.parseLong(next());
		}

		public Double nextDouble() {
			return Double.parseDouble(next());
		}
	}

	public static int[] inputArr(int n, InputReader in) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = in.nextInt();
		}
		return a;
	}

	public static int[] inputArrFrom1(int n, InputReader in) {
		int[] a = new int[n + 1];
		for (int i = 1; i <= n; i++) {
			a[i] = in.nextInt();
		}
		return a;
	}

	public static void printArr(int[] a, PrintWriter out) {
		if (a.length > 0) {
			for (int i = 0; i < a.length - 1; ++i) {
				out.print(a[i] + " ");
			}
			out.println(a[a.length - 1]);
		}
	}

	public static long gcd(long a, long b) {
		while (b > 0) {
			long c = a;
			a = b;
			b = c % b;
		}
		return a;
	}

	// C(n,m)=C(n,n-m）。（n≥m)
	// Cn0+Cn1+...+Cnn = 2^n
}