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.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    static class pair implements Comparable<pair> {
        String presuf;
        int indx;

        public pair(int cc, String s) {
            presuf = s;
            indx = cc;
        }

        public int compareTo(pair o) {
            if (presuf.length() > o.presuf.length())
                return 1;
            if (presuf.length() == o.presuf.length())
                return 0;
            else return -1;
        }

    }


    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        PrintWriter out = new PrintWriter(System.out);



        st=new StringTokenizer(br.readLine());
        long n= Long.parseLong(st.nextToken());
        int k=Integer.parseInt(st.nextToken());

        LinkedList<Integer>l=new LinkedList<>();
        int c=1;
        while (n>0){
            if (n%2==1)
                l.add(c);
            c*=2;
            n/=2;
        }
        int v=l.size();
        int x=0;
        String s="";
        if(l.size()>k)
            out.println("NO");
        else {
            while (l.size() < k && l.size() != 0) {
                if (l.getFirst() == 1) {
                    x++;
                     l.removeFirst();
                    k--;
                } else {
                    int f = l.removeFirst();
                    l.add(f / 2);
                    l.add(f / 2);

                }
            }

            if (l.size() != k)
                out.println("NO");
            else {
                out.println("YES");
                for (int i = 0; i <x; i++) {
                    out.print(1 + " ");

                }
                while (l.size() > 1)
                    out.print(l.removeFirst() + " ");
                out.print(l.removeFirst());
            }
        }


        out.flush();

    }


}