Contest Duration: - (local time) (120 minutes)
C - Product and GCD /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

N 個の 1 以上の整数 a_1, a_2, ..., a_N があります． a_1, a_2, ..., a_N の値はわかりませんが，a_1 \times a_2 \times ... \times a_N = P がわかっています．

a_1, a_2, ..., a_N の最大公約数として考えられるもののうち，最も大きいものを求めてください．

### 制約

• 1 \leq N \leq 10^{12}
• 1 \leq P \leq 10^{12}

### 入力

N P


### 入力例 1

3 24


### 出力例 1

2


### 入力例 2

5 1


### 出力例 2

1


a_i は正の整数なので，a_1 = a_2 = a_3 = a_4 = a_5 = 1 以外にはありえません．

### 入力例 3

1 111


### 出力例 3

111


### 入力例 4

4 972439611840


### 出力例 4

206


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


### 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