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)

N, P = gets.split(/ /).collect{|n| n.to_i}

if N == 1
	puts P
else
	
	MAX = 10 ** 6
	
	p_table = [true] * (MAX + 1)
	
	(2..10**6).each{|n|
		next unless p_table[n]
		x = n + n
		while x < MAX
			p_table[x] = false
			x += n
		end
	#	print "#{n} "
	}
	p_list = []
	
	(2..10**6).each{|n|
		if p_table[n]
			p_list << n
		end
	}
	
	i = p_list.length - 1
	
	f_table = {}
	
	num = P
	while i >= 0 && num > 1
		f = p_list[i]
		if f <= num
			while true
				if num % f == 0
					num = num / f
					if count = f_table[f]
						f_table[f] = count + 1
					else
						f_table[f] = 1
					end
				else
					break
				end
			end
		end
		
		i -= 1
	end
	
	answer = 1
	f_table.each{|f, count|
		if count >= N
			answer *= (f ** (count / N))
		end
	}
	
	puts answer
end