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.lang.Math;
import java.util.*;
import java.lang.*;

public class Powers2 {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        HashMap<Integer,Integer> pownum = new HashMap<Integer, Integer>();
        int count = 0;
        int comp = n;
        Stack<Integer> poword = new Stack<Integer>();
        ArrayList<Integer> temp = new ArrayList<Integer>();
        for (int i = 31; i >= 0; i--){
            if (java.lang.Math.pow(2,i) <= comp){
                pownum.put((int)java.lang.Math.pow(2,i),1);
                comp -= java.lang.Math.pow(2,i);
                ( temp).add((int)Math.pow(2,i));
                count++;
            }
        }
        for (int i = temp.size()-1; i >= 0; i--){
            poword.add(temp.get(i));
        }
        boolean foundsol = true;
        if (count > k){
            foundsol = false;
        }
        while(count < k){
            int foc = poword.pop();
            if (foc == 1){
                foundsol = false;
                break;
            }
            pownum.put(foc,pownum.get(foc)-1);
            if (!pownum.containsKey(foc/2)){
                pownum.put(foc/2,0);
                (poword).add(foc/2);
            }
            pownum.put(foc/2,pownum.get(foc/2)+2);
            count++;
            if (pownum.get(foc) == 0){
                pownum.remove(foc);
            }else{
                (poword).add(foc);
            }
        }
        if (foundsol){
            System.out.println("YES");
            Iterator it = pownum.entrySet().iterator();
            while (it.hasNext()) {
                Map.Entry pair = (Map.Entry)it.next();
                for (int i = 0; i < (int)pair.getValue(); i++){
                    System.out.print(pair.getKey()+" ");
                }
                it.remove();
            }
        }else{
            System.out.println("NO");
        }

    }
}