Integer Approximation
Time Limit: 1 Second Memory Limit: 32768 KB
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 PI 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 file 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).
Process to the end of file.
Output
Output file must contain two integers, N and D, separated by space.
Sample Input
3.14159265358979 10000
Sample Output
355 113Submit
Source: Northeastern Europe 2001, Far-Eastern Subregion