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.Arrays;
import java.util.Scanner;

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