Powers Of Two
Description
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 $1, 2, 4, 8, 16, \dots$.
You are given two positive integers $n$ and $k$. Your task is to represent $n$ as the sum of exactly $k$ powers of two.
The only line of the input contains two integers $n$ and $k$ ($1 \le n \le 10^9$, $1 \le k \le 2 \cdot 10^5$).
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.
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.
Samples
9 4
YES
1 2 2 4
8 1
YES
8
5 1
NO
3 7
NO