Calvin has a math assignment at school where he has to evaluate a lot of expressions. Calvin decides to not to waste much of his time. There are ${M}$ expressions overall. By looking at Susie’s answers, Calvin has figured that the answers to all questions form a non decreasing sequence.

He decides that all his answers are going to be between ${1}$ and $N$ (inclusive). He fills his answer sheet with a random non-decreasing sequence of length ${M}$ where each element is between ${1}$ and $N$.

Here is the part where the real problem starts for Calvin. He does not want to choose a large value of $N$, because, he will have a lot of options to choose from. Also, if he chooses a very small value of $N$, a lot of answers would become equal and the teacher will become suspicious.

If $x=\text{max}_{1\leq i\leq N}(f(i))$, f(i) being the frequency or number of times ${i}$ occurs in the sequence of ${M}$ values he picked. Calvin wants to find out expected value of $\boldsymbol{x}$. Help him solve the problem.

For example, if $M=3$ & $N=3$, the possible sequences are:

1 1 1 (x = 3)
1 1 2 (x = 2)
1 1 3 (x = 2)
1 2 2 (x = 2)
1 2 3 (x = 1)
1 3 3 (x = 2)
2 2 2 (x = 3)
2 2 3 (x = 2)
2 3 3 (x = 2)
3 3 3 (x = 3)

expected value of $x=2.2$

Input Format

The first line contains an integer ${T}$ which refers to the number of test cases. ${T}$ lines follow, each containing $2$ numbers, ${M}$ and $N$ for the corresponding test cases.

Constraints

$1\leq T\leq15$

$1\leq M\leq250$

$1\leq N\leq10^9$

Output Format

Output ${T}$ lines, each containing answer to the corresponding test case. Error of upto $10^{-3}$ is allowed.

Sample Input

4
1 5
3 3
2 9
9 6

Sample Output

1.0000000000
2.2000000000
1.2000000000
4.3146853147

Explanation

For second testcase we have

$\begin{aligned}
&$\text{Seq}\quad\text{Freq}$ \
& $111\quad 3$ \
&$112\quad2$ \
&$113\quad 2$ \
&$122\quad 2$ \
&$123\quad1$\
&$133\quad 2$ \
&$222\quad3$ \
&$223\quad2$ \
&$233\quad 2$ \
&$333\quad 3$
\end{aligned}$

$\begin{aligned}E(x)&=\sum P_x\times x\\ &=P_1+2P_2+3P_3\\ &=\frac{1}{10}+\frac{2\times6}{10}+\frac{3\times3}{10}\\ &=\frac{22}{10}\end{aligned}$

见题面

见题面