Drawing Marbles

Input

Consists of multiple test cases. The first line of each test case contains the number of colors $col$ ( $1 \leq col \leq 50$ 1 \le \text{col} \le 50) and the number $n$ . The second line contains $col$ integers $c_{1}$ c_1, $c_{2}$ c_2, $\dots$ , $c_{col}$ c_{\text{col}}, where $c_{i}$ c_i ( $1 \leq c_{i} \leq 50$ 1 \le c_i \le 50) is the number of marbles of color $i$ . It is known that $1 \leq n \leq c_{1} + c_{2} + \dots + c_{col}$ 1 \le n \le c_1 + c_2 + \ldots + c_{\text{col}}.

Output

For each test case print on a separate line the probability that all marbles drawn will be the same color. Print the probabilities with $4$ digits after the decimal point.

Examples

Example 1

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