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 TwoPower {
    public static void main(String [] args) {
        Solver s = new Solver();
        s.solve();
    }
}

class Solver {
    Reader in = new Reader ();
    Writer out = new Writer ();

    void solve () {
        int n = in.nextInt();
        int k = in.nextInt();

        Stack <Integer> s = new Stack <> ();
        for(int i = 31; i >= 0; i--) {
            if(((n >> i) & 1) == 1) {
                s.push(i);
            }
        }
        if(k < s.size() || k > n) {
            out.writeln("NO");
        } else {
            out.writeln("YES");
            while(s.size() < k) {
                if(s.peek() == 0) {
                    out.write("1 ");
                    s.pop();
                    --k;
                } else {
                    int x = s.peek();
                    s.pop();
                    s.push(x-1);
                    s.push(x-1);
                }
            }
            while(!s.isEmpty()) {
                out.write(1 << s.peek());
                out.write(' ');
                s.pop();
            }
            out.writeln("");
        }
        out.flush();
    }   
}

class Reader {
    private StringTokenizer a;
    private BufferedReader b;
    Reader () {
        a = null;
        try {
            b = new BufferedReader (new InputStreamReader (System.in)); // for file IO, replace this with new FileReader ("in.txt")
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
    public String next () {
        while(a == null || !a.hasMoreTokens()) {
            try {
                a = new StringTokenizer (b.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return a.nextToken();
    }
    public int nextInt() {
        return Integer.parseInt(this.next());
    }
    public long nextLong () {
        return Long.parseLong(this.next());
    }
    public double nextDouble () {
        return Double.parseDouble(this.next());
    }
    public String nextLine() {
        try {
            return b.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return "";
    }
}
class Writer {
    private PrintWriter a;
    private StringBuffer b;
    Writer () {
        try {
            a = new PrintWriter (System.out); // for file IO, replace this with new FileWriter ("out.txt")
        } catch (Exception e) {
            e.printStackTrace();
        }        
        b = new StringBuffer ("");
    }
    public void write (Object s) {
        b.append(s);
    }
    public void writeln(Object s) {
        b.append(s).append('\n');
    }
    public void flush () {
        a.print(b);
        a.flush();
        a.close();
    }
}
class Pair implements Comparator <Pair> {
    int first;
    int second;
    Pair  (int a, int b) {
        this.first = a;
        this.second = b;
    }
    Pair (Pair a) {
        this.first = a.first;
        this.second = a.second;
    } 
    Pair () {}
    public String toString () {
        return "[" + first + ", " + second + "]";
    }
    public int compare (Pair a, Pair b) {
        if(a.first == b.first) {
            return a.second - b.second;
        } else {
            return a.first - b.first;
        }
    }
}