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 Julia (0.5.0) (judge verdict: Accepted)

N, P = map(x -> parse(Int64,x), split(readline(STDIN)))
function primes(n)
    prime_factors = Dict{Int64, Int64}()
    divisor = 2
    
    while divisor^2 <= n
        count = 0
        while n % divisor == 0
            count += 1
            n ÷= divisor 
        end
        if count > 0
            prime_factors[divisor] = count
        end
        divisor += 1
    end
    
    if n > 1
        prime_factors[n] = 1
    end
    
    return prime_factors
end
primes_dic = primes(P)
cal_k(pair) = pair.first ^  floor(Int, pair.second / N)
answer = length(primes_dic) == 0 ? 1 : mapreduce(x->cal_k(x), *, primes_dic)
println(answer)