Using SMS today is more than a pleasing hobby. As the number of messages one sends through this
service grows, the need to type them fast is better felt. Sometimes, one wonders how fast a message can
be typed. Changing some words to their synonyms, might help type the whole message faster, if we were
able to quickly calculate the time needed for a specific message.
In the following, we assume that each message is a string of capital English letters and space character.
The letters ¡®A¡¯ through ¡®Z¡¯ are assigned to keys ¡®2¡¯ to ¡®9¡¯, as in the following figure. To type a letter, one
should press its key 1, 2, 3, or 4 times, depending on the position of the letter from left to right.
If two consecutive letters of the message are mapped to one key, one should wait for
the first letter to be fixed on the screen and then use the key again to type the second
one. For instance, to type the letter ¡®X¡¯, one should press ¡®9¡¯ twice. If the next letter of
the message is not on the same key, one can continue to type the rest of the message.
Otherwise, one has to wait for some time, so that the typed ¡®X¡¯ is fixed, and then the
next letter (¡®W¡¯, ¡®X¡¯, ¡®Y¡¯, or ¡®Z¡¯) can be typed. To type whitespace, we use the key ¡®1¡¯.
As there is no letter mapped to the key ¡®1¡¯, the whitespace needs no time to be fixed.
You are given the time needed to press any key, and the time one should wait for a letter to be fixed.
Your program should find the minimum time needed to type a nonempty string, given the above rules.
The input file contains multiple test cases. The first line of the input, contains t, the number of test cases
that follow. Each of the following t blocks, describes a test case.
The first line of each block contains p and w (1 <= p,w <= 1000), which show the amount of time in
milliseconds for pressing a letter and waiting for it to be fixed, respectively. The second line contains
a non-empty string of length at most 1000, consisting of spaces or capital English letters. There is no
leading or trailing spaces in a line.
For each test case, output one line showing the time needed to type the message in milliseconds.
Regional Tehran 2005