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 Main {
    // For fast input output
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            try {
                br = new BufferedReader(new FileReader("input.txt"));
                PrintStream out = new PrintStream(new FileOutputStream("output.txt"));
                System.setErr(new PrintStream(new FileOutputStream("error.txt")));
                System.setOut(out);
            } catch (Exception e) {
                br = new BufferedReader(new InputStreamReader(System.in));
            }
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    // end of fast i/o code
    static StringBuilder str = new StringBuilder("");

    public static void main(String[] args) {
        FastReader reader = new FastReader();
        int n = reader.nextInt();
        int k = reader.nextInt();
        ArrayList<Integer> res = new ArrayList<Integer>();
        for (int i = 0; i < 31; i++) {
            if ((n & 1) == 1)
                res.add((int) Math.pow(2, i));
            n = n >> 1;
        }
        //System.err.println(res);
        int count = res.size();
        if (count > k) {
            System.out.println("NO");
            return;
        }
        int i = 0;
        while(count<k)
        {
            if(i==res.size())
            {
                System.out.println("NO");
                return;
            }
            if(res.get(i)<2)
                i++;
            else
            {
                res.set(i, res.get(i)/2);
                res.add(res.get(i));
                //System.err.println(res);
                count++;
            }    
        }
        System.out.println("YES");
        for(int el: res)
            System.out.print(el+" ");
    }
}