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You are given a list of lowercase English letters. For a given integer , you can select any indices (assume -based indexing) with a uniform probability from the list.

Find the probability that at least one of the indices selected will contain the letter: ''.

Input Format

The input consists of three lines. The first line contains the integer , denoting the length of the list. The next line consists of space-separated lowercase English letters, denoting the elements of the list.

The third and the last line of input contains the integer , denoting the number of indices to be selected.

Output Format

Output a single line consisting of the probability that at least one of the indices selected contains the letter:''.

Note: The answer must be correct up to 3 decimal places.

Constraints

All the letters in the list are lowercase English letters.

Sample Input

4 
a a c d
2

Sample Output

0.8333

Explanation

All possible unordered tuples of length comprising of indices from to are:

Out of these combinations, of them contain either index or index which are the indices that contain the letter ''.

Hence, the answer is .