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 $\dfrac pq$.

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

```
$r$
$N$
```

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.

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

1 3

$∣0.333−\frac{1}{3}∣=\frac{1}{3000}$. There is no 0≤p≤q≤33,gcd(p,q)=1 such that $∣0.333−\frac{p}{q}∣<\frac{1}{3000}$, so print 1 3.

2 5

$∣0.45−\frac{1}{2}∣=∣0.45−\frac{2}{5}∣=\frac{1}{20}$. There is no 0≤p≤q≤5,gcd(p,q)=1 such that $∣0.45−\frac{p}{q}∣<\frac{1}{20}$, and we have $\frac{1}{2}>\frac{2}{5}$, so print 2 5.

71 226

$∣0.314159265358979323−\frac{71}{226}∣=\frac{3014435336501}{113000000000000000000}$.