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.lang.reflect.Array;
import java.util.*;
public class PowersOfTwo {

    public static void main(String[] args){
        PrintWriter pr=new PrintWriter(System.out);
        Scanner scan=new Scanner(System.in);
        int n=scan.nextInt();
        int k=scan.nextInt();
        PriorityQueue<Integer> pq=new PriorityQueue<>(Comparator.reverseOrder());
        String s=Integer.toBinaryString(n);
        String s1="";
        for(int i= s.length()-1;i>=0;i--)
            s1+=s.charAt(i);

        for(int i=0;i<s1.length();i++){
            if(s1.charAt(i)=='1')
                pq.add((int)Math.pow(2,i));
        }
        if(pq.size()>k){
            System.out.println("NO");
            return;
        }
        while(pq.size()!=k){
            int m=pq.remove();
            pq.add(m/2);
            pq.add(m/2);
            if(m==1 && (pq.size()+1)!=k){
                System.out.println("NO");
                return;
            }
        }
        System.out.println("YES");
        while(!pq.isEmpty()){
            System.out.print(pq.remove()+" ");
        }




    }
}