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.*;
import java.util.*;

//solution classes here

public class Code {

    //main solution here

    static Scanner sc = new Scanner(System.in);
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) throws IOException {
        int n = sc.nextInt();
        int k = sc.nextInt();
        int count=0;
        Deque<Integer> a=new ArrayDeque<>();
        for(int i=31;i>=0;i--) {
            if((n>>i&1)==1) {
                a.add(1<<i);
                count++;
            }
        }

        if(count<=k && k<=n) {
            out.println("YES");
            while(k>a.size()) {
                if(a.peek()>1) {
                    int val = a.pop();
                    a.add(val/2);
                    a.add(val/2);
                }
                else {
                    a.pop();
                    a.add(1);
                }
            }

            for(int it: a)
                out.print(a.pop()+" ");

        }
        else
            out.println("NO");

        out.flush();
        out.close();
    }

    //solution functions here


    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader fileReader) {
            br = new BufferedReader(fileReader);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
}

/* *****************************************************************************************************************************
 * I'M NOT IN DANGER, I'M THE DANGER!!!
 *
 *  94 40 49 65 21 21 106 80 92 81 679 4 61
  6 237 12 72 74 29 95 265 35 47 1 61 397
  52 72 37 51 1 81 45 435 7 36 57 86 81 72
 * *****************************************************************************************************************************
 */