Product and GCD

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

inputFormat

Input

Input is given from Standard Input in the following format:

N P

outputFormat

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

样例

5 1

1