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 $$\frac{1}{a} + \frac{1}{a+k} + \frac{1}{a+2k} + \dots$$ 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 $1 \le a\le b$ and $k \ge 1$.

Output

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