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C. Powers Of Two
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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.

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