P2614 Playing Piano on a Calculator

Xiao A discovered another hidden feature of a calculator — playing piano. 

In a certain mode of the calculator, pressing a key, for example `1`, will produce the middle pitch `Do`. Here is the key-to-pitch table. ```plain + 低音Fa < 低音So * 低音La / 低音Xi 1 中音Do 2 中音Re 3 中音Mi 4 中音Fa 5 中音So 6 中音La 7 高音Xi 8 高音Do 9 高音Re = 高音Mi % 高音Fa C 高音So M 高音La ``` Now Xiao A has obtained a piece of sheet music — we call it calculator notation, a variant of numbered musical notation (jianpu). Durations (i.e., how long you press) are recorded as follows, for example: `1` is a quarter note, taking $1$ beat. `1-` is a half note, taking $2$ beats. `1---` is a whole note, taking $4$ beats. For notes shorter than a quarter note, we use nested parentheses, for example: `(1(34(56))2)` `1` and `2` are inside one layer of parentheses, so they are eighth notes, taking $0.5$ beat. `3` and `4` are inside two layers of parentheses, so they are sixteenth notes, taking $0.25$ beat. `5` and `6` are inside three layers of parentheses, so they are thirty-second notes, taking $\dfrac{1}{8}$ beat. At most thirty-second notes will appear in the testdata; there are no shorter notes. The symbol `-` will not appear inside parentheses. Adding a dot `.` after a note means the note is extended by $1/2$ of its original duration. For example, `1-.` is $3$ beats, `1.` is $1.5$ beats, and in `(3.(45.))`, `3` is $\dfrac{3}{4}$ beat, `4` is $\dfrac{1}{4}$ beat, and `5` is $\dfrac{3}{8}$ beat. There will not be two or more consecutive dots. A whole note will not be dotted. Ignore other musical symbols. In addition, the entire score provides an integer $T$, the number of beats per minute. For readability, the score may contain arbitrary line breaks and spaces. They can be ignored when reading the input. Now Xiao A wants to know how many seconds it takes to finish playing this score.

The first line contains two integers $n, T$, the number of lines of the score and the beats per minute. The next $n$ lines contain the score.

Output a single integer: the total time in seconds needed to perform the score. If the exact time is fractional, round down to an integer.

- Sample Explanation For the first sample, there are $28$ quarter notes and $2$ half notes, totaling $32$ beats. With $60$ beats per minute, the total time is $32$ seconds. - Constraints For $40\%$ of the testdata, the characters `(`, `)`, and `.` do not appear. For $100\%$ of the testdata, $1 \le n \le 100,\ 50 \le T \le 200$, and each line contains at most $100$ characters. Translated by ChatGPT 5