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.*;

public class Main{
    public static void main(String[] args) throws Exception {
        new Main();
    }
    Main() throws Exception{
        InputReader in=new InputReader(System.in);
        PrintWriter out=new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int x=in.nextInt();
        PriorityQueue<Integer>pq=get(x);
        int k=in.nextInt();
        if(k<pq.size()||k>x){
            out.println("NO");
        }else {
            out.println("YES");
            for(int i=pq.size();i<k;i++){
                int tmp=pq.poll();
                pq.add(tmp-1);
                pq.add(tmp-1);
            }
            Iterator<Integer>it=pq.iterator();
            out.print(1<<it.next());
            while(it.hasNext()){
                out.print(" "+(1<<it.next()));
            }
            out.println();
        }
        out.flush();
    }
    PriorityQueue<Integer> get(int x){
        PriorityQueue<Integer>pq=new PriorityQueue<>(Collections.reverseOrder());
        for(int i=30;i>=0;i--){
            if((x&(1<<i))!=0)
                pq.add(i);
        }
        return pq;
    }
}
class InputReader {
    private InputStreamReader reader;
    private char[] buf;
    private int len, now;

    public InputReader(InputStream stream) {
        reader = new InputStreamReader(stream);
        buf = new char[1024];
        len = 0;
        now = 0;
    }

    public String next() throws IOException {
        if (!hasNext()) throw new NullPointerException();
        StringBuilder sb = new StringBuilder();
        while (!isSpaceChar(buf[now])) {
            sb.append(buf[now]);
            if (!move()) break;
        }
        return sb.toString();
    }

    public int nextInt() throws IOException {
        if (!hasNext()) throw new NullPointerException();
        boolean x = false;
        if (buf[now] == '-') {
            x = true;
            if (!move()) throw new NumberFormatException();
        }
        int ans = 0;
        while (!isSpaceChar(buf[now])) {
            if (isNum(buf[now])) ans = ans * 10 + buf[now] - '0';
            else throw new NumberFormatException();
            if (!move()) break;
        }
        return (x ? -1 : 1) * ans;
    }

    public String nextLine() throws IOException {
        if (!hasNextLine()) throw new NullPointerException();
        StringBuilder sb = new StringBuilder();
        while (buf[now] != '\n') {
            sb.append(buf[now]);
            if (!move()) return sb.toString();
        }
        now++;
        return sb.toString();
    }

    public long nextLong() throws IOException {
        if (!hasNext()) throw new NullPointerException();
        boolean x = false;
        if (buf[now] == '-') {
            x = true;
            if (!move()) throw new NumberFormatException();
        }
        long ans = 0;
        while (!isSpaceChar(buf[now])) {
            if (isNum(buf[now])) ans = ans * 10 + buf[now] - '0';
            else throw new NumberFormatException();
            if (!move()) break;
        }
        return (x ? -1 : 1) * ans;
    }

    public double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    public int nextHexInt() throws IOException {
        if (!hasNext()) throw new NullPointerException();
        boolean x = false;
        if (buf[now] == '-') {
            x = true;
            if (!move()) throw new NumberFormatException();
        }
        int ans = 0;
        while (!isSpaceChar(buf[now])) {
            if (isHex(buf[now])) ans = ans * 16 + toHex(buf[now]);
            else throw new NumberFormatException();
            if (!move()) break;
        }
        return (x ? -1 : 1) * ans;
    }

    public char nextChar() throws IOException {
        if (!hasNext()) throw new NullPointerException();
        char tmp = buf[now];
        move();
        return tmp;
    }
    public int next(char[] s) throws IOException {
        if (!hasNext()) throw new NullPointerException();
        int len=0;
        while (!isSpaceChar(buf[now])&&len<s.length) {
            s[len++]=buf[now];
            if (!move()) break;
        }
        return len;
    }
    public boolean hasNext() throws IOException {
        return skip();
    }

    public boolean hasNextLine() throws IOException {
        return now < len || refill();
    }

    private boolean move() throws IOException {
        now++;
        return hasNextLine();
    }

    private boolean skip() throws IOException {
        if (!hasNextLine()) return false;
        while (isSpaceChar(buf[now])) {
            if (!move()) return false;
        }
        return true;
    }

    private boolean isSpaceChar(char c) {
        return !(c >= 33 && c <= 126);
    }

    private boolean isNum(char c) {
        return c >= '0' && c <= '9';
    }

    private boolean isHex(char c) {
        return c >= '0' && c <= '9' || c >= 'A' && c <= 'F';
    }

    private int toHex(char c) {
        if (c >= '0' && c <= '9') return c - '0';
        else return c - 'A' + 10;
    }

    private boolean refill() throws IOException {
        len = reader.read(buf);
        now = 0;
        return len > 0;
    }
}