Treasure Hunt

Time limit1sMemory limit128 MB

Summary

Given a and b, find the shared limit of the arithmetic and harmonic mean iteration, which is sqrt(a b), printed to three decimals.

Level: Medium7 of 10
Topics: Math, Binary search
Solved: No attempts yet

Problem

On the way to school, Heehyun picked up a treasure map. The map said this.

Let the coordinates of the school's main gate be $(0, 0)$ .
$x_0 = a$ and $y_0 = b$ . ( $0 < b \le a$ )
$x_{n+1} = \dfrac{x_n + y_n}{2}$ , $y_{n+1} = \dfrac{2 x_n y_n}{x_n + y_n}$
Keep following the trail and the treasure turns up!

The two sequences $x_n$ and $y_n$ converge to one and the same value. That value is both the $x$ coordinate and the $y$ coordinate of the treasure. Help Heehyun and find where the treasure is.

Input

The first line contains two positive integers $a$ and $b$ , separated by a space. ( $0 < b \le a \le 10^{18}$ )

Output

Print the $x$ coordinate and the $y$ coordinate of the treasure on the first line, separated by a space.

Round both coordinates at the fourth digit after the decimal point and print exactly three digits after the decimal point. Keep trailing zeros. If the answer is the integer $6$ , write it as 6.000.

Examples5

Example 1
Input
```
1 1
```
Expected output
```
1.000 1.000
```
Example 2
Input
```
2 1
```
Expected output
```
1.414 1.414
```
Example 3
Input
```
7 1
```
Expected output
```
2.646 2.646
```
Example 4
Input
```
9 4
```
Expected output
```
6.000 6.000
```
Example 5
Input
```
3 2
```
Expected output
```
2.449 2.449
```