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 = gets.chomp.split.map(&:to_i)
ans = 1

soinsu = []
tmp = p+0
i = 2
while true
  if tmp ** (1.0/2) < i
    soinsu << tmp
    break
  end
  if tmp%i==0
    soinsu << i
    # soinsu << p/i
    tmp /= i
    # iまで調べたのだからもう一度iから調べる
  else
    i+=1
  end
end
soinsu.sort!
soinsu.uniq!

ary = []
soinsu.each do |num|
  tmp = p+0
  while true
    if num == 1
      break
    elsif tmp % (num**n)==0
      ary << num
      tmp /= num**n
    else
      break
    end
  end
end

ans = 1
ary.each do |i|
  ans *= i
end

puts ans