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.*;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Kattio in = new Kattio(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskA {
        public void solve(int testNumber, Kattio in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            
            Stack<Integer> powers = new Stack<>();
            int power = 1;
            while (n > 0) {
                while (n % 2 == 0) {
                    power *= 2;
                    n >>= 1;
                }

                
                n >>= 1;
                powers.push(power);
                power *= 2;
                --k;
            }

            if (k < 0) {
                out.println("NO");
                return ;
            }
            
            ArrayList<Integer> li = new ArrayList<>();
            while (k > 0 && !powers.empty()) {
                int pow = powers.pop();
                if (pow > 1) {
                    --k;
                    powers.push(pow >> 1);
                    powers.push(pow >> 1);
                } else {
                    li.add(pow);
                }
            }

            if (k > 0) {
                out.println("NO");
                return ;
            }

            out.println("YES");

            for (int i : li) {
                out.print (i + " ");
            }

            while (!powers.empty()) {
                out.print (powers.pop() + " ");
            }
            
        }

    }

    static class Kattio extends PrintWriter {
        private BufferedReader r;
        private String line;
        private StringTokenizer st;
        private String token;

        public Kattio(InputStream i) {
            super(new BufferedOutputStream(System.out));
            r = new BufferedReader(new InputStreamReader(i));
        }

        public Kattio(InputStream i, OutputStream o) {
            super(new BufferedOutputStream(o));
            r = new BufferedReader(new InputStreamReader(i));
        }

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

        public String next() {
            return nextToken();
        }

        private String peekToken() {
            if (token == null)
                try {
                    while (st == null || !st.hasMoreTokens()) {
                        line = r.readLine();
                        if (line == null) return null;
                        st = new StringTokenizer(line);
                    }
                    token = st.nextToken();
                } catch (IOException e) {
                }
            return token;
        }

        private String nextToken() {
            String ans = peekToken();
            token = null;
            return ans;
        }

    }
}