List all irreducible proper fractions with denominators no greater than $n$ in ascending order, and find the fraction at the $k$-th position.

A fraction $\frac{p}{q}$ is an irreducible proper fraction if and only if $1 \leq p < q$ and $\gcd(p, q) = 1$.

Input

A single line containing two positive integers $n$ and $k$, separated by a space.

Output

A single line containing two positive integers $p$ and $q$, separated by a space, representing the answer $\frac{p}{q}$.

Constraints

For $24\%$ of the data: $n \leq 10$

For $60\%$ of the data: $n \leq 100$

For $97\%$ of the data: $n \leq 1000$

For $100\%$ of the data: $2 \leq n \leq 10^7$, $1 \leq k < \sum_{i=1}^n \varphi (i)$, where $\varphi(n)$ denotes the number of positive integers less than $n$ that are coprime to $n$.

Examples

Input 1

6 5

Output 1

2 5

Input 2

666 66666

Output 2

300 607