Description

In mathematics, the square of a number $x$ is defined as $x^2 = x × x$. The square root of a positive number $x$ is defined as all values of $y$ that satisfy $y × y = x$.
Step 1: Let the initial solution $y_0 = 1$;
Step 2: Let $y_1 = \frac{y_0 + \frac{x}{y_0}}{2}$
Step 3: Let $y_2 = \frac{y_1 + \frac{x}{y_1}}{2}$
Step 4: Let $y_3 = \frac{y_2 + \frac{x}{y_2}}{2}$
...
Step n: Let $y_n = \frac{y_{n-1} + \frac{x}{y_{n-1}}}{2}$
When this process is carried out infinitely, the result will infinitely approach the true value. Of course, a computer cannot execute an infinite loop, so we can only find an approximate solution.
Given the number $x$ for which we want to find the square root and the number of iterations $n$, please use this algorithm to find the approximate value of the square root of $x$.

Input Format

The first line contains two integers $x$ ($1≤x≤10^4$) and $n$ ($1≤n≤1000$), as described in the problem.

Output Format

Output the approximate value of the square root of $x$, rounded to three decimal places.

Sample

4 10

2.000