Cosine Partition Function

Problem code: PARCOS

All submissions for this problem are available.

Chef Ciel is participating an arithmetic contest now. Why? Because of the top prize for the contest, limited edition chopsticks.

She must calculate the values f(M, N, X) of function named cosine partition function to be the first place. The cosine partition function f(M, N, X) is defined by

Examples are following:

f(1, 3, X) = cos(3X/3) = cos(X)

f(2, 3, X) = cos(0/3) cos(3X/3) + cos(X/3) cos(2X/3) + cos(2X/3) cos(X/3) + cos(3X/3) cos(0/3) = 2 cos(X/3) cos(2X/3) + 2 cos(X)

f(3, 1, X) = cos(0) cos(0) cos(X) + cos(0) cos(X) cos(0) + cos(X) cos(0) cos(0) = 3 cos(X)

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 10-6. You can safely assume the magnitude of the answer is at most 10300.

Constraints

1 <= T <= 50
1 <= M <= 1000000000 (10^9)
1 <= N <= 30
0 <= X <= 1

Sample Input

4
1 3 1.0
2 3 0
30 1 0.1
1 1 0.5

Sample Output

0.5403023059
4.0000000000
29.8501249583
0.8775825619
Author: laycurse
Tester: anton_lunyov
Editorial http://discuss.codechef.com/problems/PARCOS
Date Added: 1-09-2011
Time Limit: 2 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, FORT, FS, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, NODEJS, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TCL, TEXT, WSPC


Comments

An exactly similar problem

cupidvogel @ 2 Mar 2012 09:13 PM
An exactly similar problem had been posted on Codechef way back. I will provide the URL later.

Will be jury able to read

aircube @ 3 Mar 2012 12:51 AM
Will be jury able to read answer which printed in exponential notation, e.g 5.4030230587e-01 for first example ?

@aircube Yes, exponential

hiroto_adm @ 3 Mar 2012 02:27 PM
@aircube Yes, exponential notation like 5.4030230587e-01 will be accepted if the answers have an absolute or relative error no more than 10^(-6).

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