???Finding the Radius for an Inserted Circle

Three circles C_{a}C?a??, C_{b}C?b??, and C_{c}C?c??, all with radius $R$ and tangent to each other, are located in two-dimensional space as shown in Figure $1$. A smaller circle C_{1}C?1?? with radius R_{1}R?1?? (R_{1}<RR?1??<R) is then inserted into the blank area bounded by C_{a}C?a??, C_{b}C?b??, and C_{c}C?c?? so that C_{1}C?1?? is tangent to the three outer circles, C_{a}C?a??, C_{b}C?b??, and C_{c}C?c??. Now, we keep inserting a number of smaller and smaller circles C_{k}\ (2 \leq k \leq N)C?k?? (2≤k≤N) with the corresponding radius R_{k}R?k?? into the blank area bounded by C_{a}C?a??, C_{c}C?c?? and C_{k-1}C?k?1?? $(2\le k\le N)$, so that every time when the insertion occurs, the inserted circle C_{k}C?k?? is always tangent to the three outer circles C_{a}C?a??, C_{c}C?c?? and C_{k-1}C?k?1??, as shown in Figure $1$

Figure 1.

(Left) Inserting a smaller circle C_{1}C?1?? into a blank area bounded by the circle C_{a}C?a??, C_{b}C?b?? and C_{c}C?c??.

(Right) An enlarged view of inserting a smaller and smaller circle C_{k}C?k?? into a blank area bounded by C_{a}C?a??, C_{c}C?c?? and C_{k-1}C?k?1?? ($2\le k\le N$), so that the inserted circle C_{k}C?k?? is always tangent to the three outer circles, C_{a}C?a??, C_{c}C?c??, and C_{k-1}C?k?1??.

Now, given the parameters $R$ and $k$, please write a program to calculate the value of R_{k}R?k??, i.e., the radius of the $k?th$ inserted circle. Please note that since the value of R_kR?k?? may not be an integer, you only need to report the integer part of R_{k}R?k??. For example, if you find that R_{k}R?k?? = $1259.8998$ for some $k$, then the answer you should report is $1259$.

Another example, if R_{k}R?k?? = $39.1029$ for some $k$, then the answer you should report is $39$.

Assume that the total number of the inserted circles is no more than $10$, i.e., $N\le 10$. Furthermore, you may assume $\pi =3.14159$. The range of each parameter is as below:

$1\le k\le N$, and 10^{4} \leq R \leq 10^{7}10?4??≤R≤10?7??.

Input Format

Contains $l+3$ lines.

Line $1$: $l$ ----------------- the number of test cases, $l$ is an integer.

Line $2$: $R$ ---------------- $R$ is a an integer followed by a decimal point,then followed by a digit.

Line $3$: $k$ ---------------- test case #$1$, $k$ is an integer.

$\dots$

Line $i+2$: $k$ ----------------- test case # $i$.

$\dots$

Line $l+2$: $k$ ------------ test case #$l$.

Line $l+3$: $?1$ ---------- a constant $?1$ representing the end of the input file.

Output Format

Contains $l$ lines.

Line $1$: $k$ R_{k}R?k?? ----------------output for the value of $k$ and R_{k}R?k?? at the test case #$1$, each of which should be separated by a blank.

$\dots$

Line $i$: $k$ R_{k}R?k?? ----------------output for $k$ and the value of R_{k}R?k?? at the test case # $i$, each of which should be separated by a blank.

Line $l$: $k$ R_{k}R?k?? ----------------output for $k$ and the value ofR_{k}R?k?? at the test case # $l$, each of which should be separated by a blank.