To start the game they put several black and white pearls in one of the boxes.
Each robot has **N** moves, after which the initial set is being restored for the next game.
Each turn, the robot takes a pearl out of the box and puts one of the opposite color back.
The winner is the one who takes the white pearl on the **Nth** move.

Our robots don't like uncertainty, that's why they want to know the probability of drawing a white pearl on the Nth move. The probability is a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen). The result is a float from 0 to 1 with two decimal digits of precision (±0.01).

You are given a start set of pearls as a string that contains "b" (black) and "w" (white) and the number of the move (N). The order of the pearls does not matter.

**Input: ** The start sequence of the pearls as a string and the move number as an integer.

**Output: ** The probability for a white pearl as a float.

**Example:**

checkio('bbw', 3) == 0.48 checkio('wwb', 3) == 0.52 checkio('www', 3) == 0.56 checkio('bbbb', 1) == 0 checkio('wwbb', 4) == 0.5 checkio('bwbwbwb', 5) == 0.48

**How it is used: **
This task introduces you to the basics of probability theory and statistics.
Fun fact: regardless of the initial state, as the number of moves increases, the probability approaches 0.5!

**Precondition:**
0 < N ≤ 20

0 < |pearls| ≤ 20