题目描述

In the recent dance class, Teio has taught Special Week one formula to calculate the dance power $D(x)$:

$$d(x)=\int_0^x \frac{dt}{t^2+(a+b)t+ab}+\frac{lnb-lna}{a-b}$$

$$D(x)=\sum \limits_{i=1}^x ad(x)-bd(x)$$

As poor as Special Week's math is, for three given positive integer $a,b,x$ please help her calculate $D(x)$

输入格式

The first line contains one positive integer $T(1\\le T\\le10^5)$ indicating the number of the queries.

Then followed $T$ lines, each line contains three positive integers $a,b,x (1\\le a,b,x\\le10^9)$.

输出格式

For each query, output one number, the answer $D(x)$.

Your answer will be considered correct, if its absolute or relative error isn't greater than $10^{-6}$. Formally, let your answer be $a$, while jury's answer be $b$. Your answer will be considered correct if $\\frac{|a-b|}{max(a,b)}\\le10^{-6}$holds.

样例

3 
1 2 3 
9 8 7 
2021 4 9

0.6694306539 
-0.4517696480 
-45.4575754312