Sine Partition Function

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Chef Ciel is participating an arithmetic contest now.
Why?
Because of the top prize for the contest, a limited edition toaster oven.
She must calculate the values f(M, N, X) of function named sine partition function to be the first place.
The sine partition function f(M, N, X) is defined by
Examples are following:
f(1, 3, X) = sin(3X)
f(2, 3, X) = sin(0) sin(3X) + sin(X) sin(2X) + sin(2X) sin(X) + sin(3X) sin(0) = 2 sin(X) sin(2X)
f(3, 1, X) = sin(0) sin(0) sin(X) + sin(0) sin(X) sin(0) + sin(X) sin(0) sin(0) = 0
Ciel is a great chef, however she is not good at arithmetic.
For given M, N and X, your work is calculating the value of f(M, N, X).
Input
The first line contains an integer T, the number of test cases.
Then T test cases follow.
Each test case has 2 integers M, N and a real number X.
X has at most two digits after the decimal point.
Output
For each test case, print the value of f(M, N, X).
This value must have an absolute or relative error no more than 10^1.
You can safely assume the magnitude of the answer is at most 10^300.
Constraints
1 <= T <= 10
1 <= M <= 30
1 <= N <= 1000000000 (10^9)
0 <= X <= 6.28 < 2*PI
Sample Input
5 1 3 1.57 2 3 0 3 1 2.12 1 1 5 1 30 0.3
Sample Output
0.99999714638 0 0 0.959 0.412
Author:  laycurse 
Tester:  masked_zorro 
Editorial  http://discuss.codechef.com/problems/PARSIN 
Tags  hard, laycurse, oct11 
Date Added:  2092011 
Time Limit:  0.205966 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, PYP3, CLOJ, FS 
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