Problem Description

Arrange all reduced proper fractions whose numerator and denominator are both $\leq n$ in increasing order. The resulting sequence is called the Farey sequence.

Find the $k$-th smallest number in the Farey sequence for the given $n$.

Input Format

One line with two integers $n, k$.

Output Format

One line with two integers $p, q$, representing the answer $\frac{p}{q}$.

5 6

3 5

Hint

For $100\%$ of the testdata, $2 \leq n \leq 4 \times 10^4$, and $1 \leq k \leq$ the number of fractions that satisfy the conditions.

Translated by ChatGPT 5