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.*;

public class Main {

    static int decomposition(int n){
        int len=Integer.toBinaryString(n).length()-1;
        return len;
    }

    public static void main(String[] args) {
        Scanner scanner=new Scanner(System.in);
        int n=scanner.nextInt();
        int k=scanner.nextInt();

        PriorityQueue<Integer> list=new PriorityQueue<>((a,b)->Integer.compare(b,a));
        ArrayList<Integer> times=new ArrayList<>();
        int c=n;
        while(c>0){
            int d=decomposition(c);
            times.add(d);
            int del=1<<d;
            list.add(del);
            c-=del;
        }
        if(list.size()>k) {
            System.out.println("NO");
            return;
        }
        Collections.sort(times);
        if(list.size()==k){
            System.out.println("YES");
            list.forEach(t-> System.out.print(t+" "));
            return;
        }

        int delta=k-list.size();
        while(true){
            int top=list.peek();
            if(top==1) break;
            if(delta==0) break;
            if(delta>=top-1){
                int val=top;
                list.poll();
                for(int j=0;j<val;j++){
                    list.add(1);
                }
                delta-=(top-1);
//                break;
            }
            else{
                delta-=1;
                int val=top;
                list.poll();
                list.add(val/2);
                list.add(val/2);
            }

        }
        if(delta==0) {
            System.out.println("YES");
            list.forEach(t -> System.out.print(t + " "));
        }
        else{
            System.out.println("NO");
        }

    }

}