Tina Town is a friendly place. People there care about each other.
One day, Tina was playing the piano. The song that she was going to play consisted of $m$ notes, and the initial stamina of her is $n$. She would spend $k_i$ points stamina on the $i$-th note. Tina was a hardworking girl and she would spend all of her stamina on playing the piano.
After playing a song, she would get $ cos(k_{1}X)cos(k_{2}X) \cdot \cdot \cdot cos(k_{m}X) $ points of happiness.
Of course Tina knew she had many ways to spend all of her $n$ points of stamina to play $m$ notes. She would like to know the sum of happiness gained by all ways of playing.
Input
The first line of input contains an integer $T$, representing the number of cases.
For each test case,
the first line contains 2 integers and a real number $m$,$n$,$X$, according to the text.
$1 \leq T \leq 10,1 \leq m \leq 30,1 \leq n \leq {10}^{9},0 \leq X \leq 10$
Output
For each test case, output an one-digit decimal representing the answer.
Your answer will be judged correct if it has a difference with standard answer at most 1%.
Sample Input
3
3 1 0
2 2 0
2 3 3.1415926
Sample Output
0.0
1.0
0.0
Hint
In the first test case,Tina has no way to play the pinao.So the answer is 0.
In the second test case,The only way to play the piano is $k_1=1,k_2=1$,So the answer is $cos(0)\times cos(0)=1$
In the third test case,$k_1=1,k_2=2 ~~ or ~~ k_1=2,k_2=1$,so the ans is 0.
Note that please use radians
