CF1095C.Powers Of Two

普及/提高-

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题目描述

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.

输入格式

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

输出格式

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.

输入输出样例

输入#1
```
9 4
```
输出#1
```
YES
1 2 2 4 
```
输入#2
```
8 1
```
输出#2
```
YES
8 
```
输入#3
```
5 1
```
输出#3
```
NO
```
输入#4
```
3 7
```
输出#4
```
NO
```

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