22138_DivisionofBoard

Zephyr is a good carpenter. One day he got a large rectangular board, which he wanted to divide it into N equal-area rectangular pieces (Note that each cut is parallel to edge of the board, and will cut one existing piece into two pieces). As Zephyr is a flakey man, he preferred the N smaller pieces look like square. To each piece of wooden board, he defined a ratio P=L/S (L is the length of its longer side, S is the length of its shorter side). Zephyr wanted to minimize the sum of P of N pieces. Can you help him to figure out the minimum result?

The first line contains an integer K, which is the number of test cases.

For each test case, there will a line contains three integers x, y, N ( 1 ≤ x, y ≤ 3000, 1 ≤ N ≤ 15 ). x and y are the length and width of the board. N is the number Zephyr wanted to divide the board into.

For each test case, output a line contains the minimum sum of P of N pieces. Round the numbers in the output to 6 digits after decimal point.

2
15 20 8
34 53 14

12.000000
16.515776