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.

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.

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.

Sample Input 1

0.333
33

Sample Output 1

1 3

$\left\vert0.333-\dfrac13\right\vert=\dfrac1{3000}$.
There is no $0\leq p\leq q\leq33,\gcd(p,q)=1$ such that $\left\vert0.333-\dfrac pq\right\vert\lt\dfrac1{3000}$, so print 1 3.

Sample Input 2

0.45
5

Sample Output 2

2 5

$\left\vert0.45-\dfrac12\right\vert=\left\vert0.45-\dfrac25\right\vert=\dfrac1{20}$.
There is no $0\leq p\leq q\leq5,\gcd(p,q)=1$ such that $\left\vert0.45-\dfrac pq\right\vert\lt\dfrac1{20}$, and we have $\dfrac12\gt\dfrac25$, so print 2 5.

Sample Input 3

0.314159265358979323
10000

Sample Output 3

71 226

$\left\vert0.314159265358979323-\dfrac{71}{226}\right\vert=\dfrac{3014435336501}{113000000000000000000}$.

Sample Input 4

0.007735339533561113
7203576162

Sample Output 4

34928144 4515398949

见题面 Input 部分

见题面 Output 部分