Prime factors are ordered non-decreasingly and repeated according to multiplicity. Find the \(k\)-th factor of \(n\).

Input

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

The input satisfies:

• \(1 \le n, k \le 10^9\)

Output

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

Example

Input

633899 1

Output

7