CF71E.Nuclear Fusion

There is the following puzzle popular among nuclear physicists.

A reactor contains a set of n atoms of some chemical elements. We shall understand the phrase "atomic number" as the number of this atom's element in the periodic table of the chemical elements.

You are allowed to take any two different atoms and fuse a new one from them. That results in a new atom, whose number is equal to the sum of the numbers of original atoms. The fusion operation can be performed several times.

The aim is getting a new pregiven set of k atoms.

The puzzle's difficulty is that it is only allowed to fuse two atoms into one, it is not allowed to split an atom into several atoms. You are suggested to try to solve the puzzle.

以下是一个在核物理学家当中广为流传的谜题。

一个反应堆中包含某化学元素的 $n$ 个原子。我们将“原子序数”理解为该原子所属元素在化学元素周期表中的序号。

你可以任取两个不同的原子，将它们聚变生成一个新的原子。该新原子的原子序数等于原来两个原子原子序数之和。聚变操作可以执行多次。

目标是最终得到一个预先给定的、包含 $k$ 个原子的新集合。

该谜题的难点在于：只允许将两个原子聚变成一个原子，不允许将一个原子分裂成多个原子。建议你尝试解出这个谜题。

The first line contains two integers n and k (1 ≤ k ≤ n ≤ 17). The second line contains space-separated symbols of elements of n atoms, which are available from the start. The third line contains space-separated symbols of elements of k atoms which need to be the result of the fusion. The symbols of the elements coincide with the symbols from the periodic table of the chemical elements. The atomic numbers do not exceed 100 (elements possessing larger numbers are highly unstable). Some atoms can have identical numbers (that is, there can be several atoms of the same element). The sum of numbers of initial atoms is equal to the sum of numbers of the atoms that need to be synthesized.

第一行包含两个整数 $n$ 和 $k$（$1 \leq k \leq n \leq 17$）。
第二行包含 $n$ 个空格分隔的元素符号，表示初始可用的原子。
第三行包含 $k$ 个空格分隔的元素符号，表示聚变后需要得到的原子。
这些元素符号与化学元素周期表中的符号一致。原子序数不超过 $100$（原子序数更大的元素极不稳定）。
某些原子可能具有相同的符号（即可能存在多个同种元素的原子）。
初始原子的原子序数之和等于目标合成原子的原子序数之和。

If it is impossible to synthesize the required atoms, print "NO" without the quotes. Otherwise, print on the first line «YES», and on the next k lines print the way of synthesizing each of k atoms as equations. Each equation has the following form: "_x_1+_x_2+...+x__t->y__i", where x__j is the symbol of the element of some atom from the original set, and y__i is the symbol of the element of some atom from the resulting set. Each atom from the input data should occur in the output data exactly one time. The order of summands in the equations, as well as the output order does not matter. If there are several solutions, print any of them. For a better understanding of the output format, see the samples.

如果无法合成所需的原子，则输出不带引号的“NO”。否则，第一行输出「YES」，接下来的 k 行中，每行输出一个用于合成第 i 个目标原子的化学反应方程式。每个方程式具有如下形式：“_x_1+_x_2+...+x__t->y__i”，其中 x__j 是原始原子集合中某个原子所对应元素的化学符号，y__i 是目标原子集合中某个原子所对应元素的化学符号。输入数据中的每个原子在输出数据中必须且仅能出现一次。方程式中反应物的顺序，以及各条方程式的输出顺序均不重要。若存在多种可行方案，输出任意一种即可。有关输出格式的更直观理解，请参见样例。

The reactions from the first example possess the following form (the atomic number is written below and to the left of the element):

To find a periodic table of the chemical elements, you may use your favorite search engine.

The pretest set contains each of the first 100 elements of the periodic table at least once. You can use that information to check for misprints.

第一个示例中的核反应具有如下形式（元素左下方的数字为原子序数）：

如需查阅化学元素周期表，可使用您最常用的搜索引擎。

预测试数据集至少包含周期表中前 100 种元素中的每一种。您可以利用该信息检查是否存在印刷错误。