CF727A.Transformation: from A to B

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.

瓦西里有一个数字 $a$，他希望将其变为数字 $b$。为此，他可以执行以下两种操作：

• 将当前数字乘以 2（即，将数字 $x$ 替换为 $2\cdot x$）；
• 在当前数字右侧追加数字 1（即，将数字 $x$ 替换为 $10\cdot x + 1$）。

你需要帮助瓦西里仅使用上述操作将数字 $a$ 变为数字 $b$，或者判断这是不可能的。

注意：本题不要求最小化操作次数，只要找出任意一种将 $a$ 变为 $b$ 的方法即可。

The first line contains two positive integers a and b (1 ≤ a < b ≤ 109) — the number which Vasily has and the number he wants to have.

第一行包含两个正整数 $a$ 和 $b$（$1 ≤ a < b ≤ 10^9$）—— 分别为瓦西里当前拥有的数字和他希望得到的数字。

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 < i ≤ k).

If there are multiple answers, print any of them.

如果无法从 $a$ 得到 $b$，则输出 "NO"（不带引号）。

否则输出三行。第一行输出 "YES"（不带引号）。第二行输出一个整数 $k$ —— 变换序列的长度。第三行输出变换序列 $x_1,\,x_2,\,...,\,x_k$，其中：

• $x_1$ 应等于 $a$，
• $x_k$ 应等于 $b$，
• 对于 $1 < i \leq k$，$x_i$ 应由 $x_{i-1}$ 通过所描述的两种操作之一得到。

若存在多个答案，输出任意一个即可。