Problem p03194 (python)

Fixed submission:
# -*- coding: utf-8 -*-

from sys import stdin

n,x = [int(i) for i in stdin.readline().split()]
limit = int(x ** (1.0/n)) + 1

def devide_counter(x, p):
    count = 1
    x /= p
    while x % p == 0:
        count += 1
        x /= p
    return x, count

def factorize(x):
    ans = 1

    p = 2
    if x % p == 0:
        x, count = devide_counter(x, p)
        if count >= n:
            ans = ans * (p ** (count // n))

    for p in range(3, limit, 2):
        if x % p == 0:
            x, count = devide_counter(x, p)
            if count >= n:
                ans = ans * (p ** (count // n))
        if x < p * p:
            break
    return ans

if x == 1:
    print(1)
elif n == 1:
    print(x)
else:
    ans = factorize(x)
    print(ans)

Buggy submission (verdict: Runtime Error):
# -*- coding: utf-8 -*-

from sys import stdin
import math
from functools import reduce

primetable = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,8263,8269,8273,8287,8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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))

for i, p in enumerate(primetable):
    if p > limit:
        primetable = primetable[:i]
        break

def factorize(x, g):
    for p in primetable:
        if x % p == 0:
            p_n = math.pow(p, n)
            if x % p_n == 0:
                g = factorize(x / p_n, g)
                g.append(p)
                return g
    return g

if x == 1:
    print(1)
elif n == 1:
    print(x)
else:
    g = factorize(x, [])
    print(g)
    
    ans = reduce(lambda a,b: a*b, g)
    print(ans)