###### Category

###### Similar Problems

## 0788. Integer Approximation

###### Time limit : 1000 ms

Memory limit : 64 mb

The FORTH programming language does not
support floating-point arithmetic at all. Its author, Chuck Moore, maintains
that floating-point calculations are too slow and most of the time can be
emulated by integers with proper scaling. For example, to calculate the area
of` the circle with the radius *R* he suggests to use formula like *R* * *R* * 355 / 113,
which is in fact surprisingly accurate. The value of 355 / 113 ≈ 3.141593
is approximating the value of π with the absolute error of only about 2·10^{–7}.
You are to find the best integer approximation of a given floating-point number
*A* within a given integer limit *L*. That is, to find such two
integers *N* and *D* (1 £ *N*, *D* £ *L*) that the value of absolute error |*A* – *N*
/ *D*| is minimal.

### Input

The first line of input contains a
floating-point number *A* (0.1 £ *A* < 10) with the precision of up to 15
decimal digits. The second line contains the integer limit *L*. (1 £ *L* £ 100000).

### Output

Output must contain two integers, *N*
and *D*, separated by a space. If there are several
solutions output the one with smallest *D*.

Samples

№ |
Input |
Output |

1 |
3.14159265358979 10000 |
355 113 |

Text from: FarEastern subregional