???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 RR and
tangent to each other, are located in two-dimensional space as shown in Figure 11.
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}
2354a
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
\leq k \leq N)(2≤k≤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 11




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
\leq k \leq N2≤k≤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 RR and kk,
please write a program to calculate the value of R_{k}R​k​​,
i.e., the radius of the k-thk−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​​ = 1259.89981259.8998 for
some kk,
then the answer you should report is 12591259.

Another example, if R_{k}R​k​​ = 39.102939.1029 for
some kk,
then the answer you should report is 3939.

Assume that the total number of the inserted circles is no more than 1010,
i.e., N
\leq 10N≤10.
Furthermore, you may assume \pi
= 3.14159π=3.14159.
The range of each parameter is as below:

1
\leq k \leq N1≤k≤N,
and 10^{4}
\leq R \leq 10^{7}10​4​​≤R≤10​7​​.

Input Format

Contains l
+ 3l+3 lines.

Line 11: ll -----------------
the number of test cases, ll is
an integer.

Line 22: RR ---------------- RR is
a an integer followed by a decimal point,then followed by a digit.

Line 33: kk ----------------
test case #11, kk is
an integer.

\ldots…

Line i+2i+2: kk -----------------
test case # ii.

\ldots…

Line l
+2l+2: kk ------------
test case #ll.

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

Output Format

Contains ll lines.

Line 11: kk R_{k}R​k​​ ----------------output
for the value of kk and R_{k}R​k​​ at
the test case #11,
each of which should be separated by a blank.

\ldots…

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

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

样例输入

1
152973.6
1
-1

样例输出

1 23665

题目来源

2017
ACM-ICPC 亚洲区（南宁赛区）网络赛