Cascading Score Console

A retro arcade's scoring console keeps a single running score and updates it through a scripted chain of commands, one after another, the same way an operator would call one fluent method after the next without ever resetting the value in between. Starting from a given initial score, you must replay the command sequence in order. Five commands mutate the running score -- add a value, subtract a value, multiply by a value, divide by a value, and raise the score to an integer power -- while a sixth command, a checkpoint, asks you to record the current score without changing it. Your task is to report the score recorded at every checkpoint, in the order the checkpoints occur.

Input format

• Line 1: a single integer n, the number of commands in the chain.
• Line 2: a single real number init, the starting score.
• Each of the next n lines is one command, in one of these forms:
  • ADD x -- add x to the running score.
  • SUB x -- subtract x from the running score.
  • MUL x -- multiply the running score by x.
  • DIV x -- divide the running score by x.
  • POW k -- raise the running score to the integer power k.
  • CHECK -- record the current running score (the score itself is left unchanged).

Output format

Print one line for every CHECK command, in the order the CHECK commands appear in the input. Each line must contain the recorded score formatted to exactly 4 digits after the decimal point.

Constraints

• 1 <= n <= 1000
• The sequence contains at least one CHECK command.
• init and every operand x are real numbers (may include a sign and a fractional part) with absolute value at most 10^6.
• For every DIV x command, x != 0.
• For every POW k command, k is an integer with 0 <= k <= 10.
• The input is constructed so that the absolute value of the running score never exceeds 10^15 at any point while processing the commands, so ordinary 64-bit floating point arithmetic is always sufficient and never overflows.

5
10
ADD 5
CHECK
MUL 2
CHECK
SUB 3

15.0000
30.0000

4
2
DIV 4
POW 3
CHECK
ADD 1.5

0.1250