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.lang.*;
import java.io.*;

public class PowersOfTwo {

    public static void main(String args[]) throws IOException {
        FastReader in = new FastReader();
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        Task.solve(in, out);
        out.close();
    }

    static class Task {

        public static void solve(FastReader in, PrintWriter out) {
            long n,k;
            n=in.nextLong();
            k=in.nextLong();
            LinkedList<Long> q = new LinkedList<>();
            long d = 1;
            while(n!=0){
                if((n&1)==1){
                    q.add(d);
                }
                n>>=1;
                d<<=1;
            }
            if(q.size()>k){
                System.out.println("NO");
                return;
            }
            boolean flag = true;
            while(true){
//                System.out.println(q.size());
                if(!flag){
                    System.out.println("NO");
                    return;
                }
                flag = false;
                if(q.size()==k){
                    System.out.println("YES");
                    while(!q.isEmpty()){
                        System.out.print(q.poll()+" ");
                    }
                    return;
                }
                int c = q.size();
                while(c!=0){
                    c--;
                    if(q.size()==k){
                        break;
                    }
                    long t = q.poll();
                    if(t!=1){
                        q.add(t/2);
                        q.add(t/2);
                        flag=true;
                    }else{
                        q.add(t);
                    }
                }
            }
        }

        public static long lowerTwo(long a){
            long b=1;
            while(b<=a){
                b = b<<1;
            }
            b=b>>1;
            return b;
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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;
        }
    }
}