Sum of fractions P76024

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.