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: Wrong Answer)

def fact(n) 
  ret = []
  i = 2
  while i <= n do
    if n % i == 0
      ret << i
      n /= i
    else
      i += 1
    end
  end
  return ret
end

n, b = gets.chomp.split.map(&:to_i)

if b == 1
  puts 1
  exit
end

f = fact(b)

while true
  l = f.length
  (l/2).times do |i|
    f[i] = f[i] * f[l - i - 1]
    f.delete_at(l - i - 1)
    if l == 1
      f = [1]
      break
    end
    break if f.length == n
  end
  if l == 1
    f = [1]
    break
  end
  break if f.length == n
  f.sort!
end

puts f.inject(:gcd)