Calculator Music Duration

You are given a musical score written in a special calculator notation and an integer T representing the beats per minute (BPM). Your task is to compute the total play time in seconds required to execute the score.

The score is represented as a string and its note durations are determined as follows:

• A standalone note (any key) without extra symbols (for example, 1) represents a quarter note, which lasts for 1 beat.
• If the note is followed by one or more dashes (-), each dash increases the duration by 1 beat. For example, 1- lasts for 2 beats and 1--- lasts for 4 beats (a whole note). Note that a whole note (4 beats) will never have a dot.
• To represent notes with durations shorter than a quarter note, nested parentheses are used. A note enclosed in one pair of parentheses is an eighth note (i.e. its base duration is halved), in two pairs is a sixteenth note (divided by 4), and in three pairs is a thirty-second note (divided by 8). In general, if a note is nested in L levels of parentheses, its computed duration is multiplied by \(\frac{1}{2^L}\).
  For example, in the musical phrase (1(34(56))2):
  • The notes 1 and 2 (inside one pair) last \(\frac{1}{2}\) beat each.
  • The notes 3 and 4 (inside two pairs) last \(\frac{1}{4}\) beat each.
  • The notes 5 and 6 (inside three pairs) last \(\frac{1}{8}\) beat each.
• A note may be followed by a dot (.), which increases its duration by half of its current value. For instance, 1. lasts for \(1+\frac{1}{2}=1.5\) beats and 1-. lasts for \(2+1=3\) beats.

Arbitrary spaces and newlines in the score should be ignored.

The total play time is computed by summing the beat durations of all notes, and then using the formula:

[ \text{Total seconds} = \frac{\text{Total beats} \times 60}{T} ]

Print the total time in seconds.

inputFormat

Input consists of two lines. The first line is a string representing the musical score (which may contain spaces and newlines that should be ignored). The second line contains an integer T (beats per minute).

outputFormat

Output the total play time in seconds as a number. The output may be fractional.

sample

1
60

1