Problem p02793 (python)

Fixed submission:
def kouyaku(a,b):
    aa = max(a,b)
    bb = min(a,b)
    if bb == 0:
        return aa
    else:
        return kouyaku(bb,aa%bb)

def power(a, b):
	if b == 0:
		return 1
	elif b == 1:
		return a % 1000000007
	elif b % 2 == 0:
		return (power(a, b//2) ** 2) % 1000000007
	else:
		return (power(a, b//2) ** 2 * a) % 1000000007
 
def divide(a, b):
	return (a * power(b, 1000000005)) % 1000000007

def prime(x):
    if x < 2: return []

    primes = [i for i in range(x)]
    primes[1] = 0 # 1は素数ではない

    # エラトステネスのふるい
    for prime in primes:
        if prime > x**(1/2): break
        if prime == 0: continue
        for non_prime in range(2 * prime, x, prime): primes[non_prime] = 0

    return [prime for prime in primes if prime != 0]

primes = prime(10**6)
pd = {}
for i in range(len(primes)):
	pd[primes[i]] = i
MOD = 10**9+7
N = int(input())
A = [int(i) for i in input().split()]
K = [0]*len(primes)
for i in range(N):
	a = A[i]
	for i in range(len(primes)):
		p = primes[i]
		if a == 1:
			break
		elif p > 1000:
			K[pd[a]] = 1
			break
		else:
			cou = 0
			while a%p==0:
				a = a//p
				cou += 1
			K[i] = max(cou, K[i])
kv = 1
for i in range(len(primes)):
	kv *= power(primes[i], K[i])
	kv %= MOD
ans = 0
for i in range(N):
	ans += divide(kv, A[i])
	ans %= MOD
print(ans)

Buggy submission (verdict: Runtime Error):
def kouyaku(a,b):
    aa = max(a,b)
    bb = min(a,b)
    if bb == 0:
        return aa
    else:
        return kouyaku(bb,aa%bb)

def power(a, b):
	if b == 0:
		return 1
	elif b == 1:
		return a % 1000000007
	elif b % 2 == 0:
		return (power(a, b//2) ** 2) % 1000000007
	else:
		return (power(a, b//2) ** 2 * a) % 1000000007
 
def divide(a, b):
	return (a * power(b, 1000000005)) % 1000000007

primes = [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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7849,97859,97861,97871,97879,97883,97919,97927,97931,97943,97961,97967,97973,97987,98009,98011,98017,98041,98047,98057,98081,98101,98123,98129,98143,98179,98207,98213,98221,98227,98251,98257,98269,98297,98299,98317,98321,98323,98327,98347,98369,98377,98387,98389,98407,98411,98419,98429,98443,98453,98459,98467,98473,98479,98491,98507,98519,98533,98543,98561,98563,98573,98597,98621,98627,98639,98641,98663,98669,98689,98711,98713,98717,98729,98731,98737,98773,98779,98801,98807,98809,98837,98849,98867,98869,98873,98887,98893,98897,98899,98909,98911,98927,98929,98939,98947,98953,98963,98981,98993,98999,99013,99017,99023,99041,99053,99079,99083,99089,99103,99109,99119,99131,99133,99137,99139,99149,99173,99181,99191,99223,99233,99241,99251,99257,99259,99277,99289,99317,99347,99349,99367,99371,99377,99391,99397,99401,99409,99431,99439,99469,99487,99497,99523,99527,99529,99551,99559,99563,99571,99577,99581,99607,99611,99623,99643,99661,99667,99679,99689,99707,99709,99713,99719,99721,99733,99761,99767,99787,99793,99809,99817,99823,99829,99833,99839,99859,99871,99877,99881,99901,99907,99923,99929,99961,99971,99989,99991]

pset = set(primes)
pd = {}
for i in range(len(primes)):
	pd[primes[i]] = i
MOD = 10**9+7
N = int(input())
A = [int(i) for i in input().split()]
K = [0]*len(primes)
for i in range(N):
	a = A[i]
	for i in range(len(primes)):
		p = primes[i]
		if a == 1:
			break
		elif p > 1000:
			K[pd[a]] = max(K[pd[a]], 1)
			break
		else:
			cou = 0
			while a%p==0:
				a = a//p
				cou += 1
			K[i] = max(cou, K[i])
kv = 1
for i in range(len(primes)):
	kv *= power(primes[i], K[i])
	kv %= MOD
ans = 0
for i in range(N):
	ans += divide(kv, A[i])
	ans %= MOD
print(ans)

Buggy submission (verdict: Runtime Error):
def kouyaku(a,b):
    aa = max(a,b)
    bb = min(a,b)
    if bb == 0:
        return aa
    else:
        return kouyaku(bb,aa%bb)

def power(a, b):
	if b == 0:
		return 1
	elif b == 1:
		return a % 1000000007
	elif b % 2 == 0:
		return (power(a, b//2) ** 2) % 1000000007
	else:
		return (power(a, b//2) ** 2 * a) % 1000000007
 
def divide(a, b):
	return (a * power(b, 1000000005)) % 1000000007

primes = [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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7849,97859,97861,97871,97879,97883,97919,97927,97931,97943,97961,97967,97973,97987,98009,98011,98017,98041,98047,98057,98081,98101,98123,98129,98143,98179,98207,98213,98221,98227,98251,98257,98269,98297,98299,98317,98321,98323,98327,98347,98369,98377,98387,98389,98407,98411,98419,98429,98443,98453,98459,98467,98473,98479,98491,98507,98519,98533,98543,98561,98563,98573,98597,98621,98627,98639,98641,98663,98669,98689,98711,98713,98717,98729,98731,98737,98773,98779,98801,98807,98809,98837,98849,98867,98869,98873,98887,98893,98897,98899,98909,98911,98927,98929,98939,98947,98953,98963,98981,98993,98999,99013,99017,99023,99041,99053,99079,99083,99089,99103,99109,99119,99131,99133,99137,99139,99149,99173,99181,99191,99223,99233,99241,99251,99257,99259,99277,99289,99317,99347,99349,99367,99371,99377,99391,99397,99401,99409,99431,99439,99469,99487,99497,99523,99527,99529,99551,99559,99563,99571,99577,99581,99607,99611,99623,99643,99661,99667,99679,99689,99707,99709,99713,99719,99721,99733,99761,99767,99787,99793,99809,99817,99823,99829,99833,99839,99859,99871,99877,99881,99901,99907,99923,99929,99961,99971,99989,99991]

pset = set(primes)
pd = {}
for i in range(len(primes)):
	pd[primes[i]] = i
MOD = 10**9+7
N = int(input())
A = [int(i) for i in input().split()]
K = [0]*len(primes)
for i in range(N):
	a = A[i]
	for i in range(len(primes)):
		p = primes[i]
		if a == 1:
			break
		elif p > 1000:
			K[pd[a]] = max(K[pd[a]], 1)
		else:
			cou = 0
			while a%p==0:
				a = a//p
				cou += 1
			K[i] = max(cou, K[i])
kv = 1
for i in range(len(primes)):
	kv *= power(primes[i], K[i])
	kv %= MOD
ans = 0
for i in range(N):
	ans += divide(kv, A[i])
	ans %= MOD
print(ans)