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 a{
    static int cntBits(int n){
        int cnt=0;
        while(n>0){
            n=n&(n-1);
            cnt++;
        }
        return cnt;
    }
    public static void main(String [] args){
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int k=sc.nextInt();
        
    Queue<Integer> queue=new LinkedList<>();
    int sum=0;
    int cnt=0;
    for(int i=31;i>=0;i--){
        int mask=1<<i;
        if((mask&n)==mask){
            queue.add(mask);
            cnt++;
        }
    }

    if(k<cnt || k>n){
        System.out.println("NO");
        return ;
    }


    while(queue.size()!=k){

        int x=queue.poll();
        if(x==1){
            if((queue.size()+1)<=k)
               queue.add(x);
        }
        else if((queue.size()+2)<=k){
            queue.add(x/2);
            queue.add(x/2);
        }
        else if((queue.size()+1)<=k){
            queue.add(x/1);
        }
    }
    System.out.println("YES");
    while(!queue.isEmpty()){
        System.out.print(queue.poll()+" ");
    }

    }
}