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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.UnsupportedEncodingException;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Main {
    
    public static void main(String[] args) throws UnsupportedEncodingException, IOException, Exception {
        Reader.init(System.in);
        StringBuilder out = new StringBuilder();
        long n = Reader.nextLong();
        int k = Reader.nextInt();
        ArrayList<Long> arr = new ArrayList<Long>();
        for(long i = 1; i <= n; i += i)
            arr.add(i);
        ArrayList<Long> res = new ArrayList<Long>();
        for(int i = arr.size() - 1; i > -1 && n > 0; i--)
            while(arr.get(i) <= n) {
                n -= arr.get(i);
                res.add(arr.get(i));
            }
        if(res.size() > k) {
            System.out.println("NO");
            return;
        }
        for(int i = 0; i < res.size() && res.size() < k; i++)
            if(res.get(i) > 1) {
                res.set(i, res.get(i) / 2l);
                res.add(i, res.get(i));
                i--;
            }
        if(n == 0 && res.size() == k) {
            out.append("YES\n");
            for(Long l : res)
                out.append(l).append(' ');
            out.setCharAt(out.length() - 1, '\n');
        } else
            out.append("NO\n");
        PrintWriter pw = new PrintWriter(System.out);
        pw.print(out);
        pw.close();
    }

}

class Reader {

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init(InputStream input) throws UnsupportedEncodingException {
        reader = new BufferedReader(
                new InputStreamReader(input, "UTF-8"));
        tokenizer = new StringTokenizer("");
    }

    static void init(String url) throws FileNotFoundException {
        reader = new BufferedReader(new FileReader(url));
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static String nextLine() throws IOException {
        return reader.readLine();
    }

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

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

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