Write a program that reads triples of natural numbers a, b and k, and for each one computes and prints the result of

| + |
| + |
| + … |

for all fractions with denominator smaller than or equal to b.

Input

Input consists of several triples of natural numbers a, b and k, such that 1 ≤ a≤ b and k ≥ 1.

Output

For each triple, print in a line the result of the sum with four digits after the decimal point.

Public test cases

**Input**

1 3 1 5 5 2 5 6 2 5 7 2

**Output**

1.8333 0.2000 0.2000 0.3429

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Carlos Molina
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++ Java Python
- User solutions
- C C++ Java Python