Xjj's Touching Value

题号：NC216201
时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

Given three integers $a_{}$ , $b_{}$ , $n_{}$ , we define Xjj's touching value function as follows:

$F(x)=\frac{a\times x+b}{2^x} , x\in\{0,1,2\dots n\}$

Please calculate the maximum value of the function.

The first line of the input contains an integer , denoting the number of test cases. 

In each test case, there are three integers  and  in one line.

For each test case, output the maximum value of the function in the form of the simplest fraction.

示例1

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2
1 1 3
-1 -1 5

复制

1
-3/16

6/5, 2, -3/5 are simple fractions, but 2/1, 10/5, 1/1, 3/-5 not.