Expected Minimum Power

Input

Two positive integers $n (1 \leq n \leq 50)$ n~(1 \le n \le 50) and $x (1 \leq x \leq n)$ x~(1 \le x \le n).

Output

Print the expected value of $2^{S}$ 2^S, rounded to $4$ digits after the decimal point.

Examples

In the first test case, there is only one possible selection: ${1, 2, 3, 4}$ \{1, 2, 3, 4\}. The minimum element is $1$ , so the required value is $2^{1} = 2$ 2^1 = 2.

In the second test case, there are three equally likely selections: ${1, 2}$ , ${1, 3}$ , and ${2, 3}$ . The corresponding values of $S$ are $1$ , $1$ , and $2$ . Therefore, the average value of $2^{S}$ 2^S is

(2^{1} + 2^{1} + 2^{2}) /3 = 8/3 = 2.6666666

(2^1 + 2^1 + 2^2) / 3 = 8 / 3 = 2.6666666

Example 1

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Example 2

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