Solve the programming task below in a Python markdown code block.
There are N integers a_1, a_2, ..., a_N not less than 1. The values of a_1, a_2, ..., a_N are not known, but it is known that a_1 \times a_2 \times ... \times a_N = P.

Find the maximum possible greatest common divisor of a_1, a_2, ..., a_N.

Constraints

* 1 \leq N \leq 10^{12}
* 1 \leq P \leq 10^{12}

Input

Input is given from Standard Input in the following format:


N P


Output

Print the answer.

Examples

Input

3 24


Output

2


Input

5 1


Output

1


Input

1 111


Output

111


Input

4 972439611840


Output

206