Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3 24

Sample Output 1

2

The greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.

Sample Input 2

5 1

Sample Output 2

1

As a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.

Sample Input 3

1 111

Sample Output 3

111

Sample Input 4

4 972439611840

Sample Output 4

206

Solution in Ruby (2.3.3) (judge verdict: Accepted)

n, p = STDIN.gets.split(' ').map(&:to_i)

if n == 1
  puts p
  exit 0
end

start = (p ** (1.0 / n)).to_i + 1

gcd = 1
start.downto(2) do |i|
  product = p

  if (i ** n) > product
    next
  end

  if product % (i ** n) != 0
    next
  end

  product /= i ** n

  if product < 0
    next
  end

  gcd = i
  break
end

p gcd