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:
//    A Computer is Like a mischievous genie.
//    It will give you exactly what you ask for,
//    but not always what you want
//    A code by Rahul Verma


import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Set;
import java.util.SortedSet;
import java.util.Spliterator.OfPrimitive;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;


public class Main {



  public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

  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[] nextSArray() {
      String sr[] = null;
      try {
        sr = br.readLine().trim().split(" ");
      } catch (IOException e) {
        e.printStackTrace();
      }
      return sr;
    }

    String nextLine() {
      String str = "";
      try {
        str = br.readLine();
      } catch (IOException e) {
        e.printStackTrace();
      }

      return str;
    }
  }


  static long powmodulo(long a, long p) {
    if (p == 0)
      return 1 % mod;
    if (p == 1)
      return a % mod;
    long ans = 1;
    while (p > 0) {
      if ((p & 1) > 0) {
        ans = (ans * a) % mod;
      }
      a = (a * a) % mod;
      p = p >> 1;
    }
    return ans % mod;
  }




  static long mod = 1000000007;

  static long gcd(long a,long b)
  {
    if(a==0)
      return b;
    return  gcd(b%a,a);
  }

  static long fast_powerNumbers(long a,long n)
  {
    if(n==1)
      return a;
    long ans=fast_powerNumbers(a,n/2);
    if(n%2==0)
      return (ans*ans);
    else
      return ((ans*ans)*(a));
  }



  static void dfs_helper(int [][] arr,int i,int j,int team,int n,int m)
  {
    arr[i][j]=team;
    if(i-1>=0 && arr[i-1][j]==1)
      dfs(arr,i-1,j,team,n,m);
    if(j-1>=0 && arr[i][j-1]==1)
      dfs(arr,i,j-1,team,n,m);
    if(i+1< n && arr[i+1][j]==1)
      dfs(arr,i+1,j,team,n,m);
    if(j+1<m && arr[i][j+1]==1)
      dfs(arr,i,j+1,team,n,m);

  }

  static void dfs(int [][] arr,int i,int j,int team,int n,int m)
  {
        dfs_helper(arr,i,j,team,n,m);

  }



  public static void merge(int arr1[], int arr2[], int n, int m) {
    // code here

    int last = arr1[n-1];
    int b=m-1;
    while(b>0 && arr2[b]>last)
    {
      --b;

    }
    for(int i=b;i>=0;--i)
    {
      last=arr1[n-1];
      int j=n-2;
      for(;j>=0;--j)
      {
        if(arr2[i]<arr1[j])
        {
          arr1[j+1]=arr1[j];
        }
        else
          break;
      }
      if(j==-1)
        arr1[0]=arr2[i];
      else
        arr1[j+1]=arr2[i];
      arr2[i]=last;

      //System.out.println(Arrays.toString(arr1));
      //System.out.println(Arrays.toString(arr2));
    }



  }



    public static void main(String[] args) throws Exception {
    FastReader sc = new FastReader();

//    int t1=sc.nextInt();
//      for (int t = 0; t < t1 ; t++) {

        long n=sc.nextLong();
        int k=sc.nextInt();
        String b=Long.toBinaryString(n);
        int one=0;
      for (int i = 0; i < b.length() ; i++) {
        if(b.charAt(i)=='1')
          ++one;
      }
      if(k<one||k>n)
      {
        System.out.println("NO");
        return;
      }
        ArrayList<Long>al=new ArrayList<>();
      long temp=n;
      long bit=(long)1;

      while(bit<=temp)
      {
        if((bit&temp)!=0)
          al.add(bit);
        bit=bit<<1;

      }
      for (int i = 0; i <al.size() ; i++) {
        if(al.get(i)==1)
          continue;
        else
        {
          while(al.get(i)!=1&&al.size()!=k)
          {
            long pp=al.get(i);
            if(pp%2==0)
            {al.set(i,pp/2);
            al.add(pp/2);}
            else
            {
              al.set(i,pp-1);
              al.add((long)1);
            }
          }
        }
      }
      System.out.println("YES");
      System.out.println(al.toString().replaceAll("[\\[|\\]|,]",""));




}}


class DSU
{
  int parent[],rank[];
  DSU(int n)
  {
    parent=new int[n];
    rank=new int[n];
    for (int i = 0; i <n ; i++) {
      parent[i]=-1;
      rank[i]=1;
    }
  }

  int find(int s1)
  {
    if(parent[s1]==-1)
      return s1;

    parent[s1]=find(parent[s1]);
    return parent[s1];
  }

  void unite(int s1,int s2)
  {

    int p1 = find(s1);
    int p2=find(s2);
    if(rank[s1]>rank[s2])
    {
      parent[p2]=find(p1);
      rank[p1]+=rank[p2];
    }else
    {
      parent[p1]=p2;
      rank[p2]+=rank[p1];
    }
  }

}

class Pair
{
  int a; int b;
  Pair(int a,int b)
  {
    this.a=a;
    this.b=b;
  }
}


class Graph
{
  HashMap<Integer,ArrayList<Integer>>hm;
  Graph()
  {
    hm=new HashMap<>();
  }
  Graph(int n){

    hm=new HashMap<>();
    for (int i = 0; i <n ; i++) {
      hm.put(i,new ArrayList<Integer>());
    }
  }
  // function for adding an edge.................................................
  public void addEdge(int a,int b,boolean isDir)
  {
    if(isDir)
    {
      if(hm.containsKey(a))
      {
        hm.get(a).add(b);
      }
      else
      {
        hm.put(a,new ArrayList<>(Arrays.asList(b)));
      }
    }
    else
    {
      if(hm.containsKey(a))
      {
        hm.get(a).add(b);
      }
      else if(!hm.containsKey(a))
      {
        hm.put(a,new ArrayList<>(Arrays.asList(b)));
      }

      if(hm.containsKey(b))
      {
        hm.get(b).add(a);
      }
      else if(!hm.containsKey(b))
      {
        hm.put(b,new ArrayList<>(Arrays.asList(a)));
      }
    }
  }

  public void addWeightededge(){

}



}

// out.println(al.toString().replaceAll("[\\[|\\]|,]",""));