Pizza Placement

Sangeon's regular pizza place is known for right triangular tables and perfectly circular pizzas. When an order comes in from a table, the owner walks over to that table and keeps making pizzas until the table is full.

Each time the owner makes one more pizza, he follows the same rule. He considers every circle that does not overlap a pizza already on the table (touching is allowed) and that is tangent to at least two of the three sides of the table, then he puts the pizza on the largest such circle. A pizza never hangs over the edge of the table.

The legs of the table have lengths $a$ and $b$. Find the area of the $k$-th pizza placed on it.

The first line contains the number of test cases $T$ ($1 \le T \le 10000$).

Each of the next $T$ lines holds one test case as three integers $a$, $b$, $k$ separated by spaces. $a$ and $b$ are the lengths of the two legs of the right triangle, and $k$ says which pizza to measure. ($1 \le a, b \le 10^9$, $1 \le k \le 100$)

For each test case, print the area of the $k$-th pizza on its own line.

Write the area in scientific notation: one digit, a decimal point, exactly four digits after rounding, then the letter e, the sign of the exponent, and a two digit exponent. This is the format that printf("%.4e", x) in C and "%.4e" % x in Python produce. For example, an area equal to pi is printed as 3.1416e+00.