Write \(n\) as a non-decreasing sequence of prime factors with multiplicity and find its \(k\)-th element.

Input

One line containing \(n\) and \(k\).

The input satisfies:

• \(1 <= n, k <= 10^9\)

Output

Print the \(k\)-th prime factor, or -1 if fewer than \(k\) factors exist.

Example

Input

28 3

Output

7