Transformation: from A to B

题意翻译

给你一个数，你可以对他执行2种操作 1.将这个数乘2 2.在这个数末尾加上1个1 求任意一种方案使a变成b（**不需要次数最少**），如果不行，输出NO，否则输出YES，并输出任意一组解。

题目描述

Vasily has a number $ a $ , which he wants to turn into a number $ b $ . For this purpose, he can do two types of operations: - multiply the current number by $ 2 $ (that is, replace the number $ x $ by $ 2·x $ ); - append the digit $ 1 $ to the right of current number (that is, replace the number $ x $ by $ 10·x+1 $ ). You need to help Vasily to transform the number $ a $ into the number $ b $ using only the operations described above, or find that it is impossible. Note that in this task you are not required to minimize the number of operations. It suffices to find any way to transform $ a $ into $ b $ .

输入输出格式

输入格式

The first line contains two positive integers $ a $ and $ b $ ( $ 1<=a&lt;b<=10^{9} $ ) — the number which Vasily has and the number he wants to have.

输出格式

If there is no way to get $ b $ from $ a $ , print "NO" (without quotes). Otherwise print three lines. On the first line print "YES" (without quotes). The second line should contain single integer $ k $ — the length of the transformation sequence. On the third line print the sequence of transformations $ x_{1},x_{2},...,x_{k} $ , where: - $ x_{1} $ should be equal to $ a $ , - $ x_{k} $ should be equal to $ b $ , - $ x_{i} $ should be obtained from $ x_{i-1} $ using any of two described operations ( $ 1&lt;i<=k $ ). If there are multiple answers, print any of them.

输入输出样例

输入样例 #1

2 162

输出样例 #1

YES
5
2 4 8 81 162 

输入样例 #2

4 42

输出样例 #2

NO

输入样例 #3

100 40021

输出样例 #3

YES
5
100 200 2001 4002 40021