Find x such that Ax+Bsin(x)=C.

Input

The first line denotes T (number of test cases). 3T integers follow denoting A,B and C for every test case. (A >= B > 0). All Integers are less than 100000.

Output

T real numbers rounded to 6 digits one in each line.

Example

Input:
1
1 1 20

Output:
19.441787