Ax+Bsin(x)=C II

Time limit2sMemory limit512 MB

Summary

Find the unique positive x with Ax + B sin(x) = C, given 0 < B <= A, and print it to nine decimals.

Level: Medium4 of 10
Topics: Binary search, Math
Solved: No attempts yet

Problem

You are given integers $A$ , $B$ , and $C$ . Write a program that finds the solution $x$ of the equation $Ax + B\sin(x) = C$ .

The constraints give $0 < B \le A$ , so the left side grows as $x$ grows. The equation therefore has exactly one solution, and that solution is positive because $C > 0$ .

Input

The first line contains the integers $A$ , $B$ , and $C$ , separated by spaces. ( $0 < B \le A \le 100{,}000$ , $0 < C \le 100{,}000$ )

Output

Print $x$ on the first line, rounded at the tenth digit after the decimal point so that exactly nine digits follow the decimal point. Keep a trailing zero instead of dropping it, so nine digits always appear after the decimal point.

Examples2

Example 1
Input
```
1 1 20
```
Expected output
```
19.441786710
```
Example 2
Input
```
100000 1 1
```
Expected output
```
0.000010000
```