Problem p02793 (python)

Fixed submission:
import collections
import math
n = int(input())
ai = [int(i) for i in input().split()]

mod = 10**9+7

if n == 1:
    print(1)
    exit()
    
    
# 素因数分解、辞書で返すやつ
# mathをimportする
def prime(n):
    factor = {}
    tmp = int(math.sqrt(n)) + 1
    for num in range(2, tmp):
        while n % num == 0:
            n //= num
            if not num in factor.keys():
                factor[num] = 1
            else:
                factor[num] += 1
        if num > n:
            break
    if n != 1:
        if not n in factor.keys():
            factor[n] = 1
        else:
            factor[n] += 1
    return factor


dic = {}
for a in ai:
    pr = prime(a)
    for num, count in pr.items():
        if not num in dic.keys():
            dic[num] = count
        else:
            if dic[num] < count:
                dic[num] = count

kari = 1
for num,count in dic.items():
    kari *= pow(num,count,mod)
    kari %= mod

kari_old = kari
ans = 0

for i in range(n):
    kari = kari_old
    #com_ab_new = copy.deepcopy(com_ab)
    #print(com_ab,com_ab_new)
    #kari = 1
    #for j in range(kosu):
    #kari *= pow(sosu_li[j][0],com_ab[sosu_li[j][0]],mod)
    kari *= pow(ai[i],mod-2,mod)
    ans += kari
    ans %= mod
    #print(ans)
    #print(ans)
        
print(ans)

Buggy submission (verdict: Runtime Error):
import collections
import math
import numpy as np
n = int(input())
ai = [int(i) for i in input().split()]

mod = 10**9+7

if n == 1:
    print(1)
    exit()
    
    
# 素因数分解、辞書で返すやつ
# mathをimportする
def prime(n):
    factor = {}
    tmp = int(math.sqrt(n)) + 1
    for num in range(2, tmp):
        while n % num == 0:
            n //= num
            if not num in factor.keys():
                factor[num] = 1
            else:
                factor[num] += 1
        if num > n:
            break
    if n != 1:
        if not n in factor.keys():
            factor[n] = 1
        else:
            factor[n] += 1
    return factor


dic = {}
for a in ai:
    pr = prime(a)
    for num, count in pr.items():
        if not num in dic.keys():
            dic[num] = count
        else:
            if dic[num] < count:
                dic[num] = count

kari = 1
for num,count in dic.items():
    kari *= pow(num,count,mod)

kari_old = kari
ans = 0

for i in range(n):
    kari = kari_old
    #com_ab_new = copy.deepcopy(com_ab)
    #print(com_ab,com_ab_new)
    pr = prime(ai[i])
    #kari = 1
    #for j in range(kosu):
    #kari *= pow(sosu_li[j][0],com_ab[sosu_li[j][0]],mod)
    for num,count in pr.items():
        kari *= pow(pow(num,count,mod),mod-2,mod)
    ans += kari
    ans %= mod
    #print(ans)
    #print(ans)
        
print(ans)

Buggy submission (verdict: Runtime Error):
import collections
import math
import numpy as np
n = int(input())
ai = [int(i) for i in input().split()]

num = 10**6+1

mod = 10**9+7

if n == 1:
    print(1)
    exit()
    
    
# 素因数分解、辞書で返すやつ
# mathをimportする
def prime(n):
    factor = {}
    tmp = int(math.sqrt(n)) + 1
    for num in range(2, tmp):
        while n % num == 0:
            n //= num
            if not num in factor.keys():
                factor[num] = 1
            else:
                factor[num] += 1
        if num > n:
            break
    if n != 1:
        if not n in factor.keys():
            factor[n] = 1
        else:
            factor[n] += 1
    return factor


pri_li = []

for i in range(n):
    pri_li.append(collections.Counter(prime(ai[i])))
com_ab = [0]*(num)

dic = {}
for a in ai:
    pr = prime(a)
    for num, count in pr.items():
        if not num in dic.keys():
            dic[num] = count
        else:
            if dic[num] < count:
                dic[num] = count

kari = 1
for num,count in dic.items():
    kari *= pow(num,count,mod)

kari_old = kari
ans = 0

for i in range(n):
    kari = kari_old
    #com_ab_new = copy.deepcopy(com_ab)
    #print(com_ab,com_ab_new)
    keys = pri_li[i].keys()
    #kari = 1
    #for j in range(kosu):
    #    kari *= pow(sosu_li[j][0],com_ab[sosu_li[j][0]],mod)
    for j in keys:
        kari *= pow(pow(j,pri_li[i][j],mod),mod-2,mod)
    ans += kari
    ans %= mod
    #print(ans)
        
print(ans)

Buggy submission (verdict: Runtime Error):
import collections
import math
import numpy as np
n = int(input())
ai = [int(i) for i in input().split()]

num = 10**6+1

mod = 10**9+7

if n == 1:
    print(1)
    exit()
    
"""    
def seachPrimeNum(N):
    max = int(np.sqrt(N))
    seachList = [i for i in range(2,N+1)]
    primeNum = []
    while seachList[0] <= max:
        primeNum.append(seachList[0])
        tmp = seachList[0]
        seachList = [i for i in seachList if i % tmp != 0]
    primeNum.extend(seachList)
    return primeNum
"""
def primes(N):
    sieve = [1]*(N+1)
    sieve[:2] = [0, 0]
    P = []
    for i in range(2, N+1):
        if sieve[i] == 1:
            P.append(i)
            for j in range(2*i, N+1, i):
                sieve[j] = i
    return P,sieve

def prime_factorize(n,sieve):
    P = []
    while n != 1:
        #print(sieve[n],n)
        if sieve[n] == 1:
            P.append(n)
            break
        else:
            P.append(sieve[n])
            n //= sieve[n]
    return P
"""
def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a
"""
pri_li = []

prime,sieve = primes(num)

for i in range(n):
    pri_li.append(collections.Counter(prime_factorize(ai[i],sieve)))
com_ab = [0]*(num)

sosu_li = [[i,0] for i in range(num)]
kosu = 0

for i in range(n):
    #print(len(b_li[i]))
    keys = pri_li[i].keys()
    #print(keys)
    for j in keys:
        #print(sosu_li)
        if sosu_li[j][1] == 0:
            sosu_li[j][1] = 1
            kosu += 1
        com_ab[j] = max(com_ab[j],pri_li[i][j])

sosu_li.sort(reverse=True,key=lambda x: x[1])
"""
for i in range(10**3):
    if com_ab[i] > 0:
        com_num *= pow(i,com_ab[i],mod)
"""
ans = 0

kari = 1

for j in range(kosu):
    kari *= pow(sosu_li[j][0],com_ab[sosu_li[j][0]],mod)

kari_old = kari

for i in range(n):
    kari = kari_old
    #com_ab_new = copy.deepcopy(com_ab)
    #print(com_ab,com_ab_new)
    keys = pri_li[i].keys()
    #kari = 1
    #for j in range(kosu):
    #    kari *= pow(sosu_li[j][0],com_ab[sosu_li[j][0]],mod)
    for j in keys:
        kari *= pow(pow(j,pri_li[i][j],mod),mod-2,mod)
    ans += kari
    ans %= mod
    #print(ans)
        
print(ans)

Buggy submission (verdict: Runtime Error):
n = int(input())
ai = [int(i) for i in input().split()]

num = 10**6+1

mod = 10**9+7

if n == 1:
    print(1)
    exit()

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

pri_li = []

for i in range(n):
    pri_li.append(collections.Counter(prime_factorize(ai[i])))

com_ab = [0]*(num)

sosu_li = [[i,0] for i in range(num)]
kosu = 0

for i in range(n):
    #print(len(b_li[i]))
    keys = pri_li[i].keys()
    #print(keys)
    for j in keys:
        #print(sosu_li)
        if sosu_li[j][1] == 0:
            sosu_li[j][1] = 1
            kosu += 1
        com_ab[j] = max(com_ab[j],pri_li[i][j])

sosu_li.sort(reverse=True,key=lambda x: x[1])
"""
for i in range(10**3):
    if com_ab[i] > 0:
        com_num *= pow(i,com_ab[i],mod)
"""
ans = 0

kari = 1

for j in range(kosu):
    kari *= pow(sosu_li[j][0],com_ab[sosu_li[j][0]],mod)

kari_old = kari

for i in range(n):
    kari = kari_old
    #com_ab_new = copy.deepcopy(com_ab)
    #print(com_ab,com_ab_new)
    keys = pri_li[i].keys()
    #kari = 1
    #for j in range(kosu):
    #    kari *= pow(sosu_li[j][0],com_ab[sosu_li[j][0]],mod)
    for j in keys:
        kari *= pow(pow(j,pri_li[i][j],mod),mod-2,mod)
    ans += kari
    ans %= mod
    #print(ans)
        
print(ans)

Buggy submission (verdict: Runtime Error):
import fractions
import collections
import copy

n = int(input())
ai = [int(i) for i in input().split()]

num = 10**3

mod = 10**9+7

if n == 1:
    print(1)
    exit()

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

pri_li = []

for i in range(n):
    pri_li.append(collections.Counter(prime_factorize(ai[i])))

com_ab = [0]*(num)

sosu_li = [[i,0] for i in range(10**6+1)]

kosu = 0

for i in range(n):
    #print(len(b_li[i]))
    keys = pri_li[i].keys()
    #print(keys)
    for j in keys:
        #print(sosu_li)
        if sosu_li[j][1] == 0:
            sosu_li[j][1] = 1
            kosu += 1
        com_ab[j] = max(com_ab[j],pri_li[i][j])

sosu_li.sort(reverse=True,key=lambda x: x[1])
exit()
"""
for i in range(10**3):
    if com_ab[i] > 0:
        com_num *= pow(i,com_ab[i],mod)
"""
ans = 0

for i in range(n):
    com_ab_new = copy.deepcopy(com_ab)
    #print(com_ab,com_ab_new)
    keys = pri_li[i].keys()
    for j in keys:
        com_ab_new[j] -= pri_li[i][j]
    kari = 1
    for j in range(kosu):
        kari *= pow(sosu_li[j][0],com_ab_new[sosu_li[j][0]],mod)
    ans += kari
    ans %= mod
    #print(ans)
        
print(ans)

Buggy submission (verdict: Runtime Error):
import fractions
import collections
import copy

n = int(input())
ai = [int(i) for i in input().split()]

num = 10**3

mod = 10**9+7

if n == 1:
    print(1)
    exit()

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

pri_li = []

for i in range(n):
    pri_li.append(collections.Counter(prime_factorize(ai[i])))

com_ab = [0]*(num)

sosu_li = [[i,0] for i in range(10**6+1)]

kosu = 0

for i in range(n):
    #print(len(b_li[i]))
    keys = pri_li[i].keys()
    #print(keys)
    for j in keys:
        #print(sosu_li)
        if sosu_li[j][1] == 0:
            sosu_li[j][1] = 1
            kosu += 1
        com_ab[j] = max(com_ab[j],pri_li[i][j])

sosu_li.sort(reverse=True,key=lambda x: x[1])

"""
for i in range(10**3):
    if com_ab[i] > 0:
        com_num *= pow(i,com_ab[i],mod)
"""
ans = 0

for i in range(n):
    com_ab_new = copy.deepcopy(com_ab)
    #print(com_ab,com_ab_new)
    keys = pri_li[i].keys()
    for j in keys:
        com_ab_new[j] -= pri_li[i][j]
    kari = 1
    for j in range(kosu):
        kari *= pow(sosu_li[j][0],com_ab_new[sosu_li[j][0]],mod)
    ans += kari
    ans %= mod
    #print(ans)
        
print(ans)

Buggy submission (verdict: Runtime Error):
import fractions
import collections
import copy

n = int(input())
ai = [int(i) for i in input().split()]

num = 10**5

mod = 10**9+7

if n == 1:
    print(1)
    exit()

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

pri_li = []

for i in range(n):
    pri_li.append(collections.Counter(prime_factorize(ai[i])))

com_ab = [0]*(num)

for i in range(n):
    #print(len(b_li[i]))
    keys = pri_li[i].keys()
    #print(keys)
    for j in keys:
        com_ab[j] = max(com_ab[j],pri_li[i][j])

"""
for i in range(10**3):
    if com_ab[i] > 0:
        com_num *= pow(i,com_ab[i],mod)
"""
ans = 0

for i in range(n):
    com_ab_new = copy.deepcopy(com_ab)
    #print(com_ab,com_ab_new)
    keys = pri_li[i].keys()
    for j in keys:
        com_ab_new[j] -= pri_li[i][j]
    kari = 1
    for j in range(num):
        if com_ab_new[j] > 0:
            kari *= pow(j,com_ab_new[j],mod)
    ans += kari
    ans %= mod
    #print(ans)
        
print(ans)

Buggy submission (verdict: Runtime Error):
import fractions
import collections
import copy

n = int(input())
ai = [int(i) for i in input().split()]

num = 10**4

mod = 10**9+7

if n == 1:
    print(1)
    exit()

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

pri_li = []

for i in range(n):
    pri_li.append(collections.Counter(prime_factorize(ai[i])))

com_ab = [0]*(num)

for i in range(n):
    tmp = 1
    #print(len(b_li[i]))
    keys = pri_li[i].keys()
    #print(keys)
    for j in keys:
        com_ab[j] = max(com_ab[j],pri_li[i][j])

"""
for i in range(10**3):
    if com_ab[i] > 0:
        com_num *= pow(i,com_ab[i],mod)
"""
ans = 0
exit()
for i in range(n):
    com_ab_new = copy.deepcopy(com_ab)
    #print(com_ab,com_ab_new)
    keys = pri_li[i].keys()
    for j in keys:
        com_ab_new[j] -= pri_li[i][j]
    kari = 1
    for j in range(num):
        if com_ab_new[j] > 0:
            kari *= pow(j,com_ab_new[j],mod)
    ans += kari
    ans %= mod
    #print(ans)
        
print(ans)

Buggy submission (verdict: Runtime Error):
import fractions
import collections
import copy

n = int(input())
ai = [int(i) for i in input().split()]

num = 10**3+100

mod = 10**9+7

if n == 1:
    print(1)
    exit()

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

pri_li = []

for i in range(n):
    pri_li.append(collections.Counter(prime_factorize(ai[i])))

com_ab = [0]*(num)

for i in range(n):
    tmp = 1
    #print(len(b_li[i]))
    keys = pri_li[i].keys()
    #print(keys)
    for j in keys:
        com_ab[j] = max(com_ab[j],pri_li[i][j])

"""
for i in range(10**3):
    if com_ab[i] > 0:
        com_num *= pow(i,com_ab[i],mod)
"""
ans = 0

for i in range(n):
    com_ab_new = copy.deepcopy(com_ab)
    #print(com_ab,com_ab_new)
    tmp = [0]*(num)
    keys = pri_li[i].keys()
    for j in keys:
        com_ab_new[j] -= pri_li[i][j]
    kari = 1
    for j in range(num):
        if com_ab_new[j] > 0:
            kari *= pow(j,com_ab_new[j],mod)
    ans += kari
    ans %= mod
    #print(ans)
        
print(ans)

Buggy submission (verdict: Runtime Error):
import fractions
import collections
import copy

n = int(input())
ai = [int(i) for i in input().split()]

num = 10**3

mod = 10**9+7

if n == 1:
    print(1)
    exit()

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

pri_li = []

for i in range(n):
    pri_li.append(collections.Counter(prime_factorize(ai[i])))

com_ab = [0]*(num)

for i in range(n):
    tmp = 1
    #print(len(b_li[i]))
    keys = pri_li[i].keys()
    #print(keys)
    for j in keys:
        com_ab[j] = max(com_ab[j],pri_li[i][j])

"""
for i in range(10**3):
    if com_ab[i] > 0:
        com_num *= pow(i,com_ab[i],mod)
"""
ans = 0

for i in range(n):
    com_ab_new = copy.deepcopy(com_ab)
    #print(com_ab,com_ab_new)
    tmp = [0]*(num)
    keys = pri_li[i].keys()
    for j in keys:
        com_ab_new[j] -= pri_li[i][j]
    kari = 1
    for j in range(num):
        if com_ab_new[j] > 0:
            kari *= pow(j,com_ab_new[j],mod)
    ans += kari
    ans %= mod
    #print(ans)
        
print(ans)

Buggy submission (verdict: Runtime Error):
import fractions
import collections
import copy

n = int(input())
ai = [int(i) for i in input().split()]

mod = 10**9+7

if n == 1:
    print(1)
    exit()

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

pri_li = []

for i in range(n):
    pri_li.append(collections.Counter(prime_factorize(ai[i])))

com_ab = [0]*(10**3)

for i in range(n):
    tmp = 1
    #print(len(b_li[i]))
    keys = pri_li[i].keys()
    #print(keys)
    for j in keys:
        com_ab[j] = max(com_ab[j],pri_li[i][j])

com_num = 1

for i in range(10**3):
    if com_ab[i] > 0:
        com_num *= pow(i,com_ab[i],mod)

ans = 0

for i in range(n):
    ans += com_num // ai[i]
    ans %= mod
print(ans)
exit()
    
pri_li0 = copy.copy(pri_li[0])

for i in range(n-1):
    pri_li[0] += pri_li[i+1]

b_li = [pri_li[0]-pri_li0]

for i in range(1,n):
    b_li.append(pri_li[0]-pri_li[i])

com = copy.copy(b_li[0])
#print(com)
for i in range(1,n):
    com &= b_li[i]
#print(com)
#exit()
for i in range(n):
    b_li[i] -= com

ans = 0
for i in range(n):
    tmp = 1
    #print(len(b_li[i]))
    keys = b_li[i].keys()
    #print(keys)
    for j in keys:
        #print(b_li[i][j])
        #exit()
        tmp *= pow(j, b_li[i][j],mod)
        tmp %= mod
    ans += tmp
    ans %= mod

print(ans%mod)

Buggy submission (verdict: Runtime Error):
import fractions

n = int(input())
ai = [int(i) for i in input().split()]


mod = 10**9+7

if n == 1:
    print(1)
    exit()

b_li = []

seki = 1

for i in range(n):
    seki *= ai[i]
    seki %= mod

for i in range(n):
    b_li.append(seki/ai[i])

t_gcd = fractions.gcd(b_li[0],b_li[1])

for i in range(n-2):
    t_gcd = int(fractions.gcd(t_gcd,b_li[i+2]))
    
ans = 0

for i in range(n):
    ans += int(seki/t_gcd/ai[i])
    
print(ans%mod)

Buggy submission (verdict: Runtime Error):
import fractions

n = int(input())
ai = [int(i) for i in input().split()]


mod = 10**9+7

if n == 1:
    print(1)
    exit()

b_li = []

seki = 1

for i in range(n):
    seki *= ai[i]

for i in range(n):
    b_li.append(seki/ai[i])

t_gcd = fractions.gcd(b_li[0],b_li[1])

for i in range(n-2):
    t_gcd = int(fractions.gcd(t_gcd,b_li[i+2]))
    
ans = 0

for i in range(n):
    ans += int(seki/t_gcd/ai[i])
    
print(ans%mod)