Problem Statement

You are given a positive real number $r$ less than $1$, and a positive integer $N$.

Among the pair of integers $(p,q)$ such that $0\leq p\leq q\leq N$ and $\gcd(p,q)=1$, find the one that minimizes $\left\vert r-\dfrac pq\right\vert$.

If multiple such pairs $(p,q)$ exist, print the one with the smallest value of $\dfrac pq$.

Constraints

• $0\lt r\lt 1$
• $r$ is given as a real number with at most $18$ decimal places.
• $1\leq N\leq 10^{10}$
• $N$ is an integer.

Input

The input is given from Standard Input in the following format:

r
N

Output

For the pair $(p,q)$ that satisfies the conditions in the problem statement, print $p$ and $q$ in this order, separated by a space, in a single line.