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: Time Limit Exceeded)

# encoding: utf-8
N, P = map(int, input().split())

# ranks = [0] * 2
# P_tmp = P
# for p in range(2, P):
#     if P_tmp % p > 0: ranks.append(0)
#     else:
#         for i_p in range(1, P):
#             if P_tmp % (p ** (i_p + 1)) > 0: break
#         ranks.append(i_p)
#         P_tmp = P_tmp // (p ** i_p)
#         if P_tmp < 2: break

# ans = 1
# for p, rank in enumerate(ranks):
#     if p < 2: continue
#     ans = ans * (p ** (rank // N))

ans = 1
P_tmp = P
for p in range(2, P):
    if P_tmp % (p ** N) == 0:
        for i_p in range(1, P):
            if P_tmp % (p ** (N * (i_p + 1))) > 0: break
        P_tmp = P_tmp // (p ** (N * i_p))
        ans = ans * (p ** i_p)
    if P_tmp < ((p + 1) ** N): break

print(ans)