The *itertools* module standardizes a core set of fast, memory efficient tools that are useful by themselves or in combination. Together, they form an *iterator algebra* making it possible to construct specialized tools succinctly and efficiently in pure *Python*.

To read more about the functions in this module, check out their documentation here.

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 .