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



Sample input:
3 24


Sample output:
2

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-

from sys import stdin
import math

primetable = 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83153,983173,983179,983189,983197,983209,983233,983239,983243,983261,983267,983299,983317,983327,983329,983347,983363,983371,983377,983407,983429,983431,983441,983443,983447,983449,983461,983491,983513,983519,983527,983531,983533,983557,983579,983581,983597,983617,983659,983699,983701,983737,983771,983777,983783,983789,983791,983803,983809,983813,983819,983849,983861,983863,983881,983911,983923,983929,983951,983987,983993,984007,984017,984037,984047,984059,984083,984091,984119,984121,984127,984149,984167,984199,984211,984241,984253,984299,984301,984307,984323,984329,984337,984341,984349,984353,984359,984367,984383,984391,984397,984407,984413,984421,984427,984437,984457,984461,984481,984491,984497,984539,984541,984563,984583,984587,984593,984611,984617,984667,984689,984701,984703,984707,984733,984749,984757,984761,984817,984847,984853,984859,984877,984881,984911,984913,984917,984923,984931,984947,984959,985003,985007,985013,985027,985057,985063,985079,985097,985109,985121,985129,985151,985177,985181,985213,985219,985253,985277,985279,985291,985301,985307,985331,985339,985351,985379,985399,985403,985417,985433,985447,985451,985463,985471,985483,985487,985493,985499,985519,985529,985531,985547,985571,985597,985601,985613,985631,985639,985657,985667,985679,985703,985709,985723,985729,985741,985759,985781,985783,985799,985807,985819,985867,985871,985877,985903,985921,985937,985951,985969,985973,985979,985981,985991,985993,985997,986023,986047,986053,986071,986101,986113,986131,986137,986143,986147,986149,986177,986189,986191,986197,986207,986213,986239,986257,986267,986281,986287,986333,986339,986351,986369,986411,986417,986429,986437,986471,986477,986497,986507,986509,986519,986533,986543,986563,986567,986569,986581,986593,986597,986599,986617,986633,986641,986659,986693,986707,986717,986719,986729,986737,986749,986759,986767,986779,986801,986813,986819,986837,986849,986851,986857,986903,986927,986929,986933,986941,986959,986963,986981,986983,986989,987013,987023,987029,987043,987053,987061,987067,987079,987083,987089,987097,987101,987127,987143,987191,987193,987199,987209,987211,987227,987251,987293,987299,987313,987353,987361,987383,987391,987433,987457,987463,987473,987491,987509,987523,987533,987541,987559,987587,987593,987599,987607,987631,987659,987697,987713,987739,987793,987797,987803,987809,987821,987851,987869,987911,987913,987929,987941,987971,987979,987983,987991,987997,988007,988021,988033,988051,988061,988067,988069,988093,988109,988111,988129,988147,988157,988199,988213,988217,988219,988231,988237,988243,988271,988279,988297,988313,988319,988321,988343,988357,988367,988409,988417,988439,988453,988459,988483,988489,988501,988511,988541,988549,988571,988577,988579,988583,988591,988607,988643,988649,988651,988661,988681,988693,988711,988727,988733,988759,988763,988783,988789,988829,988837,988849,988859,988861,988877,988901,988909,988937,988951,988963,988979,989011,989029,989059,989071,989081,989099,989119,989123,989171,989173,989231,989239,989249,989251,989279,989293,989309,989321,989323,989327,989341,989347,989353,989377,989381,989411,989419,989423,989441,989467,989477,989479,989507,989533,989557,989561,989579,989581,989623,989629,989641,989647,989663,989671,989687,989719,989743,989749,989753,989761,989777,989783,989797,989803,989827,989831,989837,989839,989869,989873,989887,989909,989917,989921,989929,989939,989951,989959,989971,989977,989981,989999,990001,990013,990023,990037,990043,990053,990137,990151,990163,990169,990179,990181,990211,990239,990259,990277,990281,990287,990289,990293,990307,990313,990323,990329,990331,990349,990359,990361,990371,990377,990383,990389,990397,990463,990469,990487,990497,990503,990511,990523,990529,990547,990559,990589,990593,990599,990631,990637,990643,990673,990707,990719,990733,990761,990767,990797,990799,990809,990841,990851,990881,990887,990889,990893,990917,990923,990953,990961,990967,990973,990989,991009,991027,991031,991037,991043,991057,991063,991069,991073,991079,991091,991127,991129,991147,991171,991181,991187,991201,991217,991223,991229,991261,991273,991313,991327,991343,991357,991381,991387,991409,991427,991429,991447,991453,991483,991493,991499,991511,991531,991541,991547,991567,991579,991603,991607,991619,991621,991633,991643,991651,991663,991693,991703,991717,991723,991733,991741,991751,991777,991811,991817,991867,991871,991873,991883,991889,991901,991909,991927,991931,991943,991951,991957,991961,991973,991979,991981,991987,991999,992011,992021,992023,992051,992087,992111,992113,992129,992141,992153,992179,992183,992219,992231,992249,992263,992267,992269,992281,992309,992317,992357,992359,992363,992371,992393,992417,992429,992437,992441,992449,992461,992513,992521,992539,992549,992561,992591,992603,992609,992623,992633,992659,992689,992701,992707,992723,992737,992777,992801,992809,992819,992843,992857,992861,992863,992867,992891,992903,992917,992923,992941,992947,992963,992983,993001,993011,993037,993049,993053,993079,993103,993107,993121,993137,993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n,x = [int(x) for x in stdin.readline().split()]

limit = math.pow(x, (1.0/n))
memo = {1: []}
for i, p in enumerate(primetable):
    if p > limit:
        primetable = primetable[:i]
        break
    memo[p] = [p]

def factorize(x, count):
    if x in memo:
        count[x] = count.get(x, 0) + 1
        return count
    for p in primetable:
        if x % p == 0:
            count[p] = count.get(p, 0) + 1
            count = factorize(x / p, count)
            return count

if x == 1:
    print(1)
elif n == 1:
    print(x)
else:
    count = factorize(x, {})
    ans = 1
    for d, c in count.items():
        if c >= n:
            cc = c // n
            ans = ans * d * cc
    print(ans)