# Scout YYF I

Time Limit: 1000MS

Memory Limit: 65536K

## Description

YYF is a couragous scout. Now he is on a dangerous mission which is to penetrate into the enemy's base. After overcoming a series difficulties, YYF is now at the start of enemy's famous "mine road". This is a very long road, on which there are numbers of mines. At first, YYF is at step one. For each step after that, YYF will walk one step with a probability of p, or jump two step with a probality of 1-p. Here is the task, given the place of each mine, please calculate the probality that YYF can go through the "mine road" safely.

## Input

The input contains many test cases ended with EOF. Each test case contains two lines. The First line of each test case is N (1 ≤ N ≤ 10) and p (0.25 ≤ p ≤ 0.75) seperated by a single blank, standing for the number of mines and the probability to walk one step. The Second line of each test case is N integer standing for the place of N mines. Each integer is in the range of [1, 100000000].

## Output

For each test case, output the probabilty in a single line with the precision to 7 digits after the decimal point.

## Sample Input

1 0.5
2
2 0.5
2 4

## Sample Output

0.5000000
0.2500000

## Source

POJ Monthly Contest - 2009.08.23, Simon