Powers Of Two

Description:

Input:

The only line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 10^9$$$, $$$1 \le k \le 2 \cdot 10^5$$$).

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 $$$b_1, b_2, \dots, b_k$$$ such that each of $$$b_i$$$ is a power of two, and $$$\sum \limits_{i = 1}^{k} b_i = n$$$. If there are multiple answers, you may print any of them.

Sample Input:

9 4

Sample Output:

YES
1 2 2 4 

Sample Input:

8 1

Sample Output:

YES
8 

Sample Input:

5 1

Sample Output:

NO

Sample Input:

3 7

Sample Output:

NO