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.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Stack;
import java.util.StringTokenizer;

//http://codeforces.com/contest/1095/problem/B
public class Main2 {

	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		XeniaAndBitOperations solver = new XeniaAndBitOperations();
//		int test = in.nextInt();
//		while (test-- > 0)
			solver.solve(1, in, out);
		out.close();
	}

	static class XeniaAndBitOperations {
		
		long MOD = 1000000007L;

		public void solve(int testNumber, InputReader in, PrintWriter out) {

			int n = in.nextInt();
			int k = in.nextInt();
			int t = n;
			LinkedList<Integer> q = new LinkedList<>();
			
			int num=1;
			while(t>0){
				int d = t&1;
				if(d>0)
					q.add(num);
				t = t>>1;
				num = num*2;
			}
			
			if(q.size()>k || k>n)
				out.println("NO");
			else{
				
				while(q.size()!=k){
					int last = q.removeLast();
					if(last>1){
						int x = last/2;
						if(x>1){
							q.add(x);
							q.add(x);
						}
						else if(x==1){
							q.addFirst(x);
							q.addFirst(x);
						}
					}
				}
				out.println("YES");
				for(Integer x: q){
					out.print(x+" ");
				}
				out.println();
			}
			
		}

	}

	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());
		}

	}
}