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.*;
import java.math.*;

public class powersOfTwo{
    public static void main(String[] args){
        long n;
        int k;
        Scanner sc = new Scanner(System.in);
        n=sc.nextLong();
        k=sc.nextInt();
        int[] arr = new int[k];
        Arrays.fill(arr, 0, k, 1);
        int sum = k;
        for(int i = k-1;i>=0;i--){
            while(sum+arr[i]<=n){
                sum+=arr[i];
                arr[i]*=2;
            }
        }
        if(sum==n){
            System.out.println("YES");
            for(int i=0;i<k;i++) System.out.print(arr[i]+" ");
        }
        else System.out.println("NO");
    }
}