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 javafx.scene.layout.Priority;

import java.io.*;
import java.lang.reflect.Array;
import java.net.Inet4Address;
import java.util.*;
import java.lang.*;
import java.util.HashMap;
import java.util.PriorityQueue;
public class templ implements Runnable {
    public class triplet implements Comparable
    {
        int f,s;
        long t;
        triplet(int f,int s,long t)
        {
            this.f=f;
            this.s=s;
            this.t=t;
        }
        public boolean equals(Object o)
        {
            triplet ob=(triplet)o;
            int ff,ss;
            long tt;
            if(o!=null)
            {
                ff=ob.f;
                ss=ob.s;
                tt=ob.t;
                if((ff==this.f)&&(ss==this.s)&&(tt==this.t))
                    return true;
            }
            return false;
        }
        public int hashCode()
        {
            return (this.f+" "+this.s+" "+this.t).hashCode();
        }
        public int compareTo(Object o)
        {
            triplet tr=(triplet)o;
            if(t>tr.t)
                return 1;
            else
                return -1;
        }
    }
    public class pair implements Comparable
    {
        int f;
        int s;
        pair(int f,int s)
        {
            this.f=f;
            this.s=s;
        }
        public boolean equals(Object o)
        {
            pair ob=(pair)o;
            int ff;
            int ss;
            if(o!=null)
            {
                ff=ob.f;
                ss=ob.s;
                if((ff==this.f)&&(ss==this.s))
                    return true;
            }
            return false;
        }
        public int hashCode()
        {
            return (this.f+" "+this.s).hashCode();
        }
        public int compareTo(Object o)
        {
            pair pr=(pair)o;
            if(s>pr.s)
                return 1;
            else if(s==pr.s)
            {
                if(f<pr.f)
                    return -1;
                else
                    return 1;
            }
            else
                return -1;
        }
    }
    static String inttobin(long x)
    {
        String s="";
        while(x!=0)
        {
            long k=x%2;
            if(k==1)
                s=s+"1";
            else
                s=s+"0";
            x=x/2;
        }
        return s;
    }
    public static void main(String args[])throws Exception
    {
        new Thread(null,new templ(),"templ",1<<27).start();
    }
    public void run() {
        try {
            InputReader in = new InputReader(System.in);
            PrintWriter out = new PrintWriter(System.out);
            int n=in.ni();
            int k=in.ni();
            String s=inttobin(n);
            PriorityQueue<Integer>pq=new PriorityQueue<>((x,y)->(y-x));
            for(int i=0;i<s.length();i++)
            {
                char c=s.charAt(i);
                if(c=='1')
                {
                    int kk=(int)Math.pow(2,i);
                    pq.add(kk);
                }
            }
            if(k<pq.size()||k>n)
                out.println("NO");
            else
            {
                out.println("YES");
                while(pq.size()<k)
                {
                    int kk=pq.remove();
                    pq.add(kk/2);
                    pq.add(kk/2);
                }
                while(!pq.isEmpty())
                    out.print(pq.remove()+" ");
            }
            out.close();
        }
        catch(Exception e){
            return;
        }
    }
    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

    }
}