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 Python (3.4.3) (judge verdict: Wrong Answer)

N, P=map(int, input().split())

s=0
R=int(P)
ls=[]
if R==1:
    ls=[1]
else:
    while s==0:
        for i in range(2,R+1):
            if P%i==0:
                P=P/i
                if P==1:
                    s=1
                ls.append(i)
                break
# print(ls)

dic={}
for a in ls:
    dic[a]=dic.get(a,0)+1
ls_dic=list(dic.items())

ans=1
for i in range(len(dic)):
    if ls_dic[i][1]>=N:
        ans*=ls_dic[i][0]
print(ans)