Loan Shark

Problem Description

A 19-year-old college student, little $L$, is in a tough financial situation and his monthly allowance is not enough to buy a smartphone. When he learns that there are lending institutions offering small loans with equal monthly installment repayments, requiring only a few hundred yuan per month, his vanity drives him to start his loan journey.

The lending institution claims that interest accrues monthly, and the borrower repays a fixed installment amount each month during the loan period.

Given the principal $n$ of little $L$'s loan, the monthly installment $m$, and the total number of months $k$ needed to pay off the loan, find the monthly interest rate $p$ of this loan.

Input Format

Three space-separated positive integers $n$, $m$, $k$, as described above.

Output Format

One real number $p$, the monthly interest rate of the loan (as a decimal). An absolute error from the standard output not exceeding $10^{-6}$ is acceptable.

Sample Input 1

1000 1200 1

Sample Output 1

0.200000

Sample Input 2

1000 100 12

Sample Output 2

0.029229

Sample Explanation

For the first sample, little $L$ borrows $1000$ yuan and pays $1200$ yuan one month later to pay off the loan. So the formula for the monthly interest rate $p$ is $1000 \times (1+p) = 1200$ or $\frac{1200}{1+p} = 1000$, giving $p = 0.200000$.

For the second sample, little $L$ borrows $1000$ yuan and pays $100$ yuan per month, paying it off after $12$ months. Due to the monthly interest rate, the amount he repays in the $k$-th month is equivalent to only $\frac{100}{(1+p)^k}$ yuan of the initial amount, and these $12$ months together repay an initial amount of $1000$ yuan, giving $p = 0.029229$.

Constraints

$1 \leq n, m \leq 10^6$, $1 \leq k \leq 300$

$0 \leq p \leq 5$

$n \leq m \times k$