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.lang.*;

public class Main {

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