C. Powers Of Twotime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA 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.InputThe 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).OutputIf 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.ExamplesInput
9 4
Output
YES
1 2 2 4 
Input
8 1
Output
YES
8 
Input
5 1
Output
NO
Input
3 7
Output
NO

9 4

YES 1 2 2 4  
['bitmasks', 'greedy', '*1400']