Problem:


Score : 500 points

Problem Statement

Given are N positive integers A_1,...,A_N.

Consider positive integers B_1, ..., B_N that satisfy the following condition.

Condition: For any i, j such that 1 \leq i < j \leq N, A_i B_i = A_j B_j holds.

Find the minimum possible value of B_1 + ... + B_N for such B_1,...,B_N.

Since the answer can be enormous, print the sum modulo (10^9 +7).

Constraints

1 \leq N \leq 10^4

1 \leq A_i \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N

Output

Print the minimum possible value of B_1 + ... + B_N for B_1,...,B_N that satisfy the condition, modulo (10^9 +7).

Sample Input 1

3
2 3 4

Sample Output 1

13

Let B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.

Sample Input 2

5
12 12 12 12 12

Sample Output 2

5

We can let all B_i be 1.

Sample Input 3

3
1000000 999999 999998

Sample Output 3

996989508

Print the sum modulo (10^9+7).



Sample input:
3
2 3 4


Sample output:
13

Submission status: Wrong Answer

Solution code:
import sys
input=sys.stdin.readline
sys.setrecursionlimit(10 ** 8)
from itertools import accumulate
from itertools import permutations
from itertools import combinations
from collections import defaultdict
from collections import Counter
import fractions
import math
from collections import deque
from bisect import bisect_left
from bisect import bisect_right
from bisect import insort_left
import itertools
from heapq import heapify
from heapq import heappop
from heapq import heappush
import heapq
from copy import deepcopy
from decimal import Decimal
alf = list("abcdefghijklmnopqrstuvwxyz")
ALF = list("ABCDEFGHIJKLMNOPQRSTUVWXYZ")
#import numpy as np
INF = float("inf")
#d = defaultdict(int)
#d = defaultdict(list)
MOD = 10**9+7
N = int(input())
A = list(map(int,input().split()))
MAX = max(A)
def primes(n):#nまでの素数を列挙0は入れちゃダメ
    is_prime = [True]*(n+1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2,int(n**(0.5)+1)):
        if not is_prime[i]:
            continue
        for j in range(i*2,n+1,i):
            is_prime[j] = False
    return is_prime
prime = primes(MAX)
pri = [i for i in range(2,MAX+1) if prime[i]]
def factorization(n): #2以上の整数n => [[素因数, 指数], ...]の2次元リストを返す
    arr = defaultdict(int)
    temp = n
    for i in range(2,int(n**0.5)+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr[i] += cnt
    if temp!=1:
        arr[temp] = 1
    if len(arr) == 0:
        arr[n] = 1
    return arr
c = factorization(A[0])
for i in range(1,N):
    nex = factorization(A[i])
    for j in pri:
        aa = max(c[j],nex[j])
        c[j] = aa
print(1)

Submission status: Wrong Answer

Solution code:
import math
MOD = 10**9+7

N = int(input())
A = list(map(int,input().split()))
A.sort()
MAX = max(A[-1],2)

C = [0 for _ in range(MAX+1)]

for a in A:
  C[a] += 1


ans = 1
P = [1 for _ in range(MAX+1)] #素数かどうか
P[0] = 0
P[1] = 0
S = [0 for _ in range(MAX+1)] #最小公倍数の素因数分解したもの
for i in range(2,MAX):
  #素数でないなら以下の手順を行わない
  if P[i] == 0:
    continue
  #エラトステネスの篩
  k = i*2
  while k <= MAX:
    P[k] = 0
    k += i
  ind = 0
  k = 1
  while k <= MAX:
    k *= i
    ind += 1
  k = k // i 
  ind -= 1
  #最大のべきを調べる
  while k > 1:
    l = k
    flag = False
    while l <= MAX:
      if C[l] > 0:
        flag = True
        break
      l += k
    if flag:
      break
    k = k // i
    ind -= 1
  S[i] = ind
  ans *= pow(i,ind,MOD)
  ans %= MOD
  
#モジュラ逆数
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    #if g != 1:
        #raise Exception('modular inverse does not exist')
    #else:
    return x % m
      
B = [0 for _ in range(MAX+1)]
ans_2 = 0
for a in A:
  if B[a] > 0:
    ans_2 += B[a]
  else:
    B[a] = modinv(a, MOD)
    ans_2 += B[a]    
  ans_2 %= MOD 

#print(ans, ans_2, P, S, B)
print((ans * ans_2) % MOD)

Submission status: Wrong Answer

Solution code:
import math
MOD = 10**9+7

N = int(input())
A = list(map(int,input().split()))

MAX = 10**6
C = [0 for _ in range(MAX+1)]
A.sort()
for a in A:
  C[a] += 1
MAX = max(A[-1],2)

ans = 1
P = [1 for _ in range(MAX+1)] #素数かどうか
P[0] = 0
P[1] = 0
S = [0 for _ in range(MAX+1)] #最小公倍数の素因数分解したもの
for i in range(2,MAX):
  #素数でないなら以下の手順を行わない
  if P[i] == 0:
    continue
  #エラトステネスの篩
  k = i*2
  while k <= MAX:
    P[k] = 0
    k += i
  ind = 0
  k = 1
  while k <= MAX:
    k *= i
    ind += 1
  k = k // i 
  ind -= 1
  #最大のべきを調べる
  while k > 1:
    l = k
    flag = False
    while l <= MAX:
      if C[l] > 0:
        flag = True
        break
      l += k
    if flag:
      break
    k = k // i
    ind -= 1
  S[i] = ind
  ans *= pow(i,ind,MOD)
  ans %= MOD
  

  
#モジュラ逆数
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    #if g != 1:
        #raise Exception('modular inverse does not exist')
    #else:
    return x % m
      
B = [0 for _ in range(MAX+1)]
ans_2 = 0
for a in A:
  if B[a] > 0:
    ans_2 += B[a]
  else:
    B[a] = modinv(a, MOD)
    ans_2 += B[a]    
  ans_2 %= MOD 

#print(ans, ans_2, P, S, B)
print((ans * ans_2) % MOD)

Submission status: Wrong Answer

Solution code:
import math
MOD = 10**9+7

N = int(input())
A = list(map(int,input().split()))

MAX = 10**6
C = [0 for _ in range(MAX+1)]
A.sort()
for a in A:
  C[a] += 1
MAX = max(A[-1],2)

ans = 1
P = [1 for _ in range(MAX+1)] #素数かどうか
P[0] = 0
P[1] = 0
lim = min(math.sqrt(MAX) + 1,MAX-1)
S = [0 for _ in range(MAX+1)] #最小公倍数の素因数分解したもの
for i in range(2,int(lim+2)):
  #素数でないなら以下の手順を行わない
  if P[i] == 0:
    continue
  #エラトステネスの篩
  k = i*2
  while k <= MAX:
    P[k] = 0
    k += i
  ind = 0
  k = 1
  while k <= MAX:
    k *= i
    ind += 1
  k = k // i 
  ind -= 1
  #最大のべきを調べる
  while k > 1:
    l = k
    flag = False
    while l <= MAX:
      if C[l] > 0:
        flag = True
        break
      l += k
    if flag:
      break
    k = k // i
    ind -= 1
  S[i] = ind
  ans *= pow(i,ind,MOD)
  ans %= MOD
    
#モジュラ逆数
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    #if g != 1:
        #raise Exception('modular inverse does not exist')
    #else:
    return x % m
      
B = [0 for _ in range(MAX+1)]
ans_2 = 0
for a in A:
  if B[a] > 0:
    ans_2 += B[a]
  else:
    B[a] = modinv(a, MOD)
    ans_2 += B[a]    
  ans_2 %= MOD 

#print(ans, ans_2, P, S, B)
print((ans * ans_2) % MOD)

Submission status: Wrong Answer

Solution code:
import math
MOD = 10**9+7

N = int(input())
A = list(map(int,input().split()))

MAX = 10**6
C = [0 for _ in range(MAX+1)]
for a in A:
  C[a] += 1

ans = 1
P = [1 for _ in range(MAX+1)] #素数かどうか
P[0] = 0
P[1] = 0
lim = math.sqrt(MAX) + 1
S = [0 for _ in range(MAX+1)] #最小公倍数の素因数分解したもの
for i in range(2,int(lim+2)):
  #素数でないなら以下の手順を行わない
  if P[i] == 0:
    continue
  #エラトステネスの篩
  k = i*2
  while k <= MAX:
    P[k] = 0
    k += i
  ind = 0
  k = 1
  while k <= MAX:
    k *= i
    ind += 1
  k = k // i 
  ind -= 1
  #最大のべきを調べる
  while k > 1:
    l = k
    flag = False
    while l <= MAX:
      if C[l] > 0:
        flag = True
        break
      l += k
    if flag:
      break
    k = k // i
    ind -= 1
  S[i] = ind
  ans *= pow(i,ind,MOD)
  ans %= MOD
    
#モジュラ逆数
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m
      
B = [0 for _ in range(MAX+1)]
ans_2 = 0
for a in A:
  if B[a] > 0:
    ans_2 += B[a]
  else:
    B[a] = modinv(a, MOD)
    ans_2 += B[a]    
  ans_2 %= MOD 

#print(ans, ans_2, P, S, B)
print((ans * ans_2) % MOD)

Submission status: Wrong Answer

Solution code:
import sys
import itertools
# import numpy as np
import time
import math
import heapq
from collections import defaultdict
sys.setrecursionlimit(10 ** 7)
 
INF = 10 ** 18
MOD = 10 ** 9 + 7
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

# map(int, input().split())

N = int(input())
A = list(map(int, input().split()))

def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)
def lcm(a, b):
    return (a * b // gcd(a, b))

l = A[0]
for i in range(1, N):
    l = lcm(l, A[i])

# ans = 0
# for a in A:
#     ans += l // a
#     ans %= MOD
# print(ans)
print(l % MOD)

Submission status: Wrong Answer

Solution code:
import sys
import itertools
# import numpy as np
import time
import math
import heapq
from collections import defaultdict
sys.setrecursionlimit(10 ** 7)
 
INF = 10 ** 18
MOD = 10 ** 9 + 7
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

# map(int, input().split())

N = int(input())
A = list(map(int, input().split()))

def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)
def lcm(a, b):
    return a * b * gcd(a, b)

l = A[0]
for i in range(1, N):
    l = lcm(l, A[i])

ans = 0
for a in A:
    ans += l // a
    ans %= MOD
print(ans)

Submission status: Wrong Answer

Solution code:
from fractions import gcd

N = int(input())
As = list(map(int, input().split()))
P = 10**9+7

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

lcm = As[0]*As[1]//gcd(As[0],As[1])
 
for i in range(2,N):
  c = gcd(lcm, As[i])
  lcm *= As[i]//c

Submission status: Wrong Answer

Solution code:
import sys,bisect,string,math,time,functools,random,fractions
from heapq import heappush,heappop,heapify
from collections import deque,defaultdict,Counter
from itertools import permutations,combinations,groupby
rep=range;R=range
def Golf():n,*t=map(int,open(0).read().split())
def I():return int(input())
def S_():return input()
def IS():return input().split()
def LS():return [i for i in input().split()]
def MI():return map(int,input().split())
def LI():return [int(i) for i in input().split()]
def LI_():return [int(i)-1 for i in input().split()]
def NI(n):return [int(input()) for i in range(n)]
def NI_(n):return [int(input())-1 for i in range(n)]
def StoLI():return [ord(i)-97 for i in input()]
def ItoS(n):return chr(n+97)
def LtoS(ls):return ''.join([chr(i+97) for i in ls])
def RA():return map(int,open(0).read().split())
def GI(V,E,ls=None,Directed=False,index=1):
    org_inp=[];g=[[] for i in range(V)]
    FromStdin=True if ls==None else False
    for i in range(E):
        if FromStdin:
            inp=LI()
            org_inp.append(inp)
        else:
            inp=ls[i]
        if len(inp)==2:
            a,b=inp;c=1
        else:
            a,b,c=inp
        if index==1:a-=1;b-=1
        aa=(a,c);bb=(b,c);g[a].append(bb)
        if not Directed:g[b].append(aa)
    return g,org_inp
def GGI(h,w,search=None,replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1):
    #h,w,g,sg=GGI(h,w,search=['S','G'],replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1) # sample usage
    mp=[boundary]*(w+2);found={}
    for i in R(h):
        s=input()
        for char in search:
            if char in s:
                found[char]=((i+1)*(w+2)+s.index(char)+1)
                mp_def[char]=mp_def[replacement_of_found]
        mp+=[boundary]+[mp_def[j] for j in s]+[boundary]
    mp+=[boundary]*(w+2)
    return h+2,w+2,mp,found
def TI(n):return GI(n,n-1)
def accum(ls):
    rt=[0]
    for i in ls:rt+=[rt[-1]+i]
    return rt
def bit_combination(n,base=2):
    rt=[]
    for tb in R(base**n):s=[tb//(base**bt)%base for bt in R(n)];rt+=[s]
    return rt
def gcd(x,y):
    if y==0:return x
    if x%y==0:return y
    while x%y!=0:x,y=y,x%y
    return y
def YN(x):print(['NO','YES'][x])
def Yn(x):print(['No','Yes'][x])
def show(*inp,end='\n'):
    if show_flg:print(*inp,end=end)

mo=10**9+7
inf=float('inf')
FourNb=[(-1,0),(1,0),(0,1),(0,-1)];EightNb=[(-1,0),(1,0),(0,1),(0,-1),(1,1),(-1,-1),(1,-1),(-1,1)];compas=dict(zip('WENS',FourNb));cursol=dict(zip('LRUD',FourNb))
l_alp=string.ascii_lowercase
#sys.setrecursionlimit(10**7)
read=sys.stdin.buffer.read;readline=sys.stdin.buffer.readline;input=lambda:sys.stdin.readline().rstrip()

########################################################################################################################################################################

## return the list of prime numbers in [2,N], using eratosthenes sieve
## around 800 ms for N = 10**6  by PyPy3 (7.3.0) @ AtCoder
def PrimeNumSet(N):
    Max = int(N**0.5)
    seachList = [i for i in range(2,N+1)]
    primeNum = []
    while seachList:
        if seachList[0] > Max:
            break
        primeNum.append(seachList[0])
        tmp = seachList[0]
        seachList = [i for i in seachList if i % tmp != 0]
    primeNum.extend(seachList)
    return primeNum


show_flg=False
show_flg=True

n=I()
a=sorted(LI())

N=10**3
prs=PrimeNumSet(N)

l=defaultdict(int)
for i in range(n):
    t=a[i]
    for p in prs:
        if t%p==0:
            c=0
            while t%p==0:
                t//=p
                c+=1
            l[p]=max(l[p],c)
    if t!=1:
        l[t]=1

ans=0
for i in range(n):
    t=a[i]
    tmp=1
    for p in prs:
        c=0
        if t%p==0:
            while t%p==0:
                t//=p
                c+=1
        tmp*=pow(p,l[p]-c,mo)
        tmp%=mo
    ans+=tmp
print(ans%mo)

Submission status: Wrong Answer

Solution code:
import sys,bisect,string,math,time,functools,random,fractions
from heapq import heappush,heappop,heapify
from collections import deque,defaultdict,Counter
from itertools import permutations,combinations,groupby
rep=range;R=range
def Golf():n,*t=map(int,open(0).read().split())
def I():return int(input())
def S_():return input()
def IS():return input().split()
def LS():return [i for i in input().split()]
def MI():return map(int,input().split())
def LI():return [int(i) for i in input().split()]
def LI_():return [int(i)-1 for i in input().split()]
def NI(n):return [int(input()) for i in range(n)]
def NI_(n):return [int(input())-1 for i in range(n)]
def StoLI():return [ord(i)-97 for i in input()]
def ItoS(n):return chr(n+97)
def LtoS(ls):return ''.join([chr(i+97) for i in ls])
def RA():return map(int,open(0).read().split())
def GI(V,E,ls=None,Directed=False,index=1):
    org_inp=[];g=[[] for i in range(V)]
    FromStdin=True if ls==None else False
    for i in range(E):
        if FromStdin:
            inp=LI()
            org_inp.append(inp)
        else:
            inp=ls[i]
        if len(inp)==2:
            a,b=inp;c=1
        else:
            a,b,c=inp
        if index==1:a-=1;b-=1
        aa=(a,c);bb=(b,c);g[a].append(bb)
        if not Directed:g[b].append(aa)
    return g,org_inp
def GGI(h,w,search=None,replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1):
    #h,w,g,sg=GGI(h,w,search=['S','G'],replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1) # sample usage
    mp=[boundary]*(w+2);found={}
    for i in R(h):
        s=input()
        for char in search:
            if char in s:
                found[char]=((i+1)*(w+2)+s.index(char)+1)
                mp_def[char]=mp_def[replacement_of_found]
        mp+=[boundary]+[mp_def[j] for j in s]+[boundary]
    mp+=[boundary]*(w+2)
    return h+2,w+2,mp,found
def TI(n):return GI(n,n-1)
def accum(ls):
    rt=[0]
    for i in ls:rt+=[rt[-1]+i]
    return rt
def bit_combination(n,base=2):
    rt=[]
    for tb in R(base**n):s=[tb//(base**bt)%base for bt in R(n)];rt+=[s]
    return rt
def gcd(x,y):
    if y==0:return x
    if x%y==0:return y
    while x%y!=0:x,y=y,x%y
    return y
def YN(x):print(['NO','YES'][x])
def Yn(x):print(['No','Yes'][x])
def show(*inp,end='\n'):
    if show_flg:print(*inp,end=end)

mo=10**9+7
inf=float('inf')
FourNb=[(-1,0),(1,0),(0,1),(0,-1)];EightNb=[(-1,0),(1,0),(0,1),(0,-1),(1,1),(-1,-1),(1,-1),(-1,1)];compas=dict(zip('WENS',FourNb));cursol=dict(zip('LRUD',FourNb))
l_alp=string.ascii_lowercase
#sys.setrecursionlimit(10**7)
read=sys.stdin.buffer.read;readline=sys.stdin.buffer.readline;input=lambda:sys.stdin.readline().rstrip()

########################################################################################################################################################################

## return the list of prime numbers in [2,N], using eratosthenes sieve
## around 800 ms for N = 10**6  by PyPy3 (7.3.0) @ AtCoder
def PrimeNumSet(N):
    Max = int(N**0.5)
    seachList = [i for i in range(2,N+1)]
    primeNum = []
    while seachList:
        if seachList[0] > Max:
            break
        primeNum.append(seachList[0])
        tmp = seachList[0]
        seachList = [i for i in seachList if i % tmp != 0]
    primeNum.extend(seachList)
    return primeNum


show_flg=False
show_flg=True

n=I()
a=sorted(LI())

N=10**3
prs=PrimeNumSet(N)

l=defaultdict(int)
for i in range(n):
    t=a[i]
    for p in prs:
        if t%p==0:
            c=0
            while t%p==0:
                t//=p
                c+=1
            l[p]=max(l[p],c)

L=1
for i,j in l.items():
    L*=i**j

ans=0
for i in range(n):
    ans+=L//a[i]
    ans%=mo

print(ans)

Submission status: Wrong Answer

Solution code:
n=int(input(""))
lista=input("").split(" ")
listso=[]
def prime(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
listso+=prime(int(lista[0]))
for i in range(1,n):
    a=int(lista[i])
    for k in listso:
        if(a%k==0):
            a/=k
    listso+=prime(a)
   
c=1
for i in listso:
    c*=i
    c%=(10**9+7)
    

s=0
for i in lista:
    s+=c/int(i)
    s%=(10**9+7)
print(int(s))

Submission status: Wrong Answer

Solution code:
import numpy as np

N=int(input())
A=np.array(list(map(int,input().split())))
mod = 10**9+7

#A = np.where(A >= mod, A % mod, A)

LCM = np.lcm.reduce(A)

print(((LCM//A) % mod).sum() % mod)

Submission status: Wrong Answer

Solution code:
import numpy as np

N=int(input())
A=np.array(list(map(int,input().split())))
mod = 10**9+7

#A = np.where(A >= mod, A % mod, A)

LCM = np.lcm.reduce(A)

print(((LCM//A) % mod).sum())

Submission status: Wrong Answer

Solution code:
import numpy as np

N=int(input())
A=np.array(list(map(int,input().split())))
mod = 10**9+7

#A = np.where(A >= mod, A % mod, A)

LCM = np.lcm.reduce(A)

print((LCM//A).sum() % mod)

Submission status: Wrong Answer

Solution code:
import numpy as np

N=int(input())
A=np.array(list(map(int,input().split())))
mod = 10**9+7

A = np.where(A >= mod, A % mod, A)

LCM = np.lcm.reduce(A)

print((LCM//A).sum() % mod)

Submission status: Wrong Answer

Solution code:
from functools import reduce

def gcd(x, y):
    if x < y:
        x, y = y, x
    while x % y != 0:
        r = x % y
        x = y
        y = r
    return y

def inv(x):
    return pow(x, MOD-2, MOD)

def lcm(a, b):
    return a * b * inv(gcd(a, b))

def addmod(a, b):
    return (a+b) % MOD
  
  
N = int(input())
a_list = list(map(int, input().split()))
MOD = 10 ** 9 + 7

l = reduce(lcm, a_list)
ans = reduce(addmod, (l*inv(a) for a in a_list))

print(ans%MOD)

Submission status: Wrong Answer

Solution code:
from functools import reduce

def gcd(x, y):
    if x < y:
        x, y = y, x
    while x % y != 0:
        r = x % y
        x = y
        y = r
    return y

def inv(x):
    return pow(x, MOD-2, MOD)

def lcm(a, b):
    return a * b * inv(gcd(a, b))

def addmod(a, b):
    return (a+b) % MOD
  
  
N = int(input())
a_list = list(map(int, input().split()))
MOD = 10 ** 9 + 7

l = reduce(lcm, a_list) % MOD
ans = reduce(addmod, (l*inv(a) for a in a_list))

print(ans%MOD)

Submission status: Wrong Answer

Solution code:
from functools import reduce

def gcd(x, y):
    if x < y:
        x, y = y, x
    while x % y != 0:
        r = x % y
        x = y
        y = r
    return y

def inv(x):
    return pow(x, MOD-2, MOD)

def lcm(a, b):
    return a * b // gcd(a, b)

def addmod(a, b):
    return (a+b) % MOD
  
  
N = int(input())
a_list = list(map(int, input().split()))
MOD = 10 ** 9 + 7

l = reduce(lcm, a_list) % MOD
ans = reduce(addmod, (l//a for a in a_list))

print(ans)

Submission status: Wrong Answer

Solution code:
from functools import reduce

def gcd(x, y):
    if x < y:
        x, y = y, x
    while x % y != 0:
        r = x % y
        x = y
        y = r
    return y

def inv(x):
    return pow(x, MOD-2, MOD)

def lcm(a, b):
    return a * b * inv(gcd(a, b))

def addmod(a, b):
    return (a+b) % MOD
  
  
N = int(input())
a_list = list(map(int, input().split()))
MOD = 10 ** 9 + 7

l = reduce(lcm, a_list) % MOD
ans = reduce(addmod, (l*inv(a) for a in a_list), 0)

print(ans)

Submission status: Wrong Answer

Solution code:
def gcd(x, y):
    if x < y:
        x, y = y, x
    while x % y != 0:
        r = x % y
        x = y
        y = r
    return y

N = int(input())
a_list = list(map(int, input().split()))
MOD = 10 ** 9 + 7

if N == 1:
    print(a_list[0])
    exit()
div = gcd(a_list[0], a_list[1])
lcm = (a_list[0] * a_list[1]) // div

for i in range(2, N):
    div = gcd(lcm, a_list[i])
    lcm = (lcm * a_list[i]) // div
    
ans = 0
for i in range(N):
    ans = (ans + lcm//a_list[i]) % MOD

print(ans)

Submission status: Wrong Answer

Solution code:
import sys
input = sys.stdin.readline
n = int(input())
num = list(map(int, input().split()))
mod = 10**9+7
num = tuple(num)

def primeFactor(N):
    i = 2
    ret = {}
    n = N
    while i*i <= n:
        k = 0
        while n % i == 0:
            n //= i
            k += 1
        if k: ret[i] = k
        i += 1 + i%2
        if i == 101 and n >= 2**20:
            def findFactorRho(N):
                def gcd(a, b):
                    while b: a, b = b, a % b
                    return a
                def f(x, c):
                    return (x * x + c) % N
                for c in range(1, 99):
                    X, d, j = [2], 1, 0
                    while d == 1:
                        j += 1
                        X.append(f(X[-1], c))
                        X.append(f(X[-1], c))
                        d = gcd(abs(X[2*j]-X[j]), N)
                    if d != N:
                        if isPrimeMR(d):
                            return d
                        elif isPrimeMR(N//d): return N//d
            while n > 1:
                if isPrimeMR(n):
                    ret[n], n = 1, 1
                else:
                    j = findFactorRho(n)
                    k = 0
                    while n % j == 0:
                        n //= j
                        k += 1
                    ret[j] = k
 
    if n > 1: ret[n] = 1
    return ret
def isPrimeMR(n):
    if n == 2:
        return True
    if n == 1 or n & 1 == 0:
        return False
    d = (n - 1) >> 1
    while d & 1 == 0:
        d >>= 1
    
    L = [2, 7, 61] if n < 1<<32 else [2, 13, 23, 1662803] if n < 1<<40 else [2, 3, 5, 7, 11, 13, 17] if n < 1<<48 else [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
    for a in L:
        t = d
        y = pow(a, t, n)
        while t != n - 1 and y != 1 and y != n - 1:
            y = (y * y) % n
            t <<= 1
 
        if y != n - 1 and t & 1 == 0:
            return False
    return True
  
lcd = dict()
for i in num:
  j = primeFactor(i)
  print(primeFactor(i))
  for x,y in j.items():
    if not x in lcd.keys():
      lcd[x] = y
    else:
      lcd[x] = max(lcd[x],y)

lc = 1
for i,j in lcd.items():
  lc *= pow(i,j,mod)
  
ans =0
for i in range(n):
  ans += lc*pow(num[i], mod-2, mod)
  ans %= mod
print(ans)

Submission status: Wrong Answer

Solution code:
from math import gcd


def ext_euc(a, b):
    if b == 0:
        return 1, 0, a
    y, x, v = ext_euc(b, a % b)
    y -= (a // b) * x
    return x, y, v


def mod_inv(a, mod):
    x, _, _ = ext_euc(a, mod)
    return x % mod


def lcm(nums, mod):
    ret = nums[0]
    for n in nums[1:]:
        d = gcd(ret, n)
        v = n * ret
        v %= mod
        v *= mod_inv(d, mod)
        v %= mod
        ret = v
    return ret


def main():
    MOD = 10 ** 9 + 7
    N = int(input())
    A = list(map(int, input().split(' ')))
    fa = A[0]
    numer = [1] * N
    denom = [1] * N
    for i, a in enumerate(A):
        if i == 0:
            continue
        d = gcd(fa, a)
        numer[i] = fa // d
        denom[i] = a // d
    m = lcm(denom, MOD)
    ans = 0
    for n, d in zip(numer, denom):
        v = n * m
        v %= MOD
        v *= mod_inv(d, MOD)
        ans += v
        ans %= MOD
    print(ans)


if __name__ == '__main__':
    main()

Submission status: Wrong Answer

Solution code:
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


n = int(input())
a = list(map(int, input().split()))
M = 10**9+7


def gcd(a, b):
    while b:
        a, b = b, a%b
    return a

def lcm(a, b):
    return a*b*pow(gcd(a,b), M-2, M)
#     return a//gcd(a, b)*b

def lcms(a):
    l = a[0]
    for num in a[1:]:
        l = lcm(l, num)
    return l

l = lcms(a)    
ans = 0
for num in a:
    ans += (l*pow(num, M-2, M))
    ans %= M
print(ans)

Submission status: Wrong Answer

Solution code:
import sys
from math import gcd

sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
f_inf = float('inf')
mod = 10 ** 9 + 7


def lcm(a, b):
    return a * b // gcd(a, b)


def resolve():
    n = int(input())
    A = list(map(int, input().split()))

    L = 1
    for a in A:
        L = lcm(L, a)
        L %= mod

    res = 0
    for a in A:
        res += L * pow(a, mod - 2, mod)
        res %= mod
    print(res)


if __name__ == '__main__':
    resolve()

Submission status: Wrong Answer

Solution code:
import sys
input = sys.stdin.readline
from collections import defaultdict


class PrimeFactor():

    def __init__(self, n):                  # エラトステネス　O(N loglog N)
        self.n = n
        self.table = list(range(n+1))
        self.table[2::2] = [2]*(n//2)
        for p in range(3, int(n**0.5) + 2, 2):
            if self.table[p] == p:
                self.table[p * p::2 * p] = [p] * ((n - p * p - 1) // (2 * p) + 1)

    def is_prime(self, x):  # 素数判定　O(1)
        if x < 2:
            return False
        return self.table[x] == x

    def prime_factors(self, x):             # 素因数分解 O(logN)
        res = []
        if x < 2:
            return res
        while self.table[x] != 1:
            res.append(self.table[x])
            x //= self.table[x]
        return res

    def prime_counter(self, x):             # 素因数分解（個数のリスト）
        res = defaultdict(int)
        if x < 2:
            return res
        while self.table[x] != 1:
            res[self.table[x]] += 1
            x //= self.table[x]
        return res

    def prime_gcd(self, X):                 # n個の最大公約数　X:n個のリスト
        exponents = self.prime_counter(X[0])
        for x in X[1:]:
            Y = self.prime_counter(x)
            for prime, exp in exponents.items():
                if Y[prime] < exp:
                    exponents[prime] = Y[prime]
        res = 1
        for prime, exp in exponents.items():
            res *= pow(prime, exp)
        return res

    def prime_lcm(self, X, mod=None):       # n個の最小公倍数　X:n個のリスト
        exponents = defaultdict(int)
        for x in X:
            for prime, exp in self.prime_counter(x).items():
                if exp > exponents[prime]:
                    exponents[prime] = exp
        res = 1
        for prime, exp in exponents.items():
            res *= pow(prime, exp, mod)
        if mod == None:
            return res
        else:
            return res % mod

mod = 10 ** 9 + 7

N = int(input())
A = set(map(int, input().split()))
A = list(A)
table = PrimeFactor(10**6)
num = table.prime_lcm(A,mod)

res = 0
for a in A:
    res += num * pow(a, mod - 2, mod)

print(res % mod)

Submission status: Wrong Answer

Solution code:
from functools import reduce
from math import gcd

MOD = 10 ** 9 + 7

_ = int(input())
la = list(map(int, input().split()))


def inv(a):
    return pow(a, MOD - 2, MOD)


def lcm(a, b):
    return (a * b // gcd(a, b))


def addmod(a, b):
    return (a + b) % MOD


l = reduce(lcm, la) % MOD
answer = reduce(addmod, (l * inv(a) for a in la))
print(answer)

Submission status: Wrong Answer

Solution code:
from functools import reduce

MOD = 10 ** 9 + 7

_ = int(input())
la = list(map(int, input().split()))


def inv(a):
    return pow(a, MOD - 2, MOD)


def gcd(a, b):
    while b:
        a, b = b, a % b
    return a


def lcm(a, b):
    return a * b * inv(gcd(a, b))


def addmod(a, b):
    return (a + b) % MOD


l = reduce(lcm, la)
answer = reduce(addmod, (l * inv(a) for a in la))
print(answer)

Submission status: Wrong Answer

Solution code:
from functools import reduce

MOD = 10 ** 9 + 7

_ = int(input())
la = list(map(int, input().split()))


def gcd(a, b):
    while b:
        a, b = b, a % b
    return a


def lcm(a, b):
    return (a * b // gcd(a, b)) % MOD


def addmod(a, b):
    return (a + b) % MOD


l = reduce(lcm, la)
answer = reduce(addmod, (l // a for a in la))
print(answer)

Submission status: Wrong Answer

Solution code:
import sys
input = sys.stdin.readline
import math

big = 10 ** 9 + 7

N = int(input())
A = list(map(int, input().split()))
num = A[0]
for i in range(1, N):
    num = num * A[i] * pow(math.gcd(num, A[i]), big-2, big)

res = 0
for a in A:
    res += num // a

print(res % big)

Submission status: Wrong Answer

Solution code:
import sys
input = sys.stdin.readline

import math

big = 10**9 + 7

N = int(input())
row_A = list(map(int, input().split()))

A = []
for a in row_A:
    A.append(a%big)


num = A[0]
set_A = set(A)

for a in set_A:
    num = num * a * pow(math.gcd(num, a),big-2,big)

res = 0
for a in A:
    res += num//a % big

print(res%big)

Submission status: Wrong Answer

Solution code:
import sys
input = sys.stdin.readline

import math

big = 10**9 + 7

N = int(input())
row_A = list(map(int, input().split()))

A = []
for a in row_A:
    A.append(a%big)


num = A[0]
for i in range(1, N):
    num = num * A[i] * pow(math.gcd(num, A[i]), big-2, big)

res = 0
for a in A:
    res += num//a % big

print(res%big)

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
import copy


mod = 10 ** 9 + 7
primes = []
for i in range(2,1002):
  for prime in primes:
    if not i % prime:
      break
  else:
    primes.append(i)

def factorize(n):
  now = n
  fct = dict()
  for prime in primes:
    cnt = 0
    if prime ** 2 > n:
      break
    while not now % prime:
      now //= prime
      cnt += 1
    if cnt:
      fct[prime] = cnt
  if now > 1:
    fct[now] = 1
  return fct


n = int(input())
a = list(map(int, input().split()))
fct_a = list()
for i in a:
  fct_a.append(factorize(i))
lcm = defaultdict(int)
for i in fct_a:
  for k,v in i.items():
    lcm[k] = max(lcm[k], v)
ans = 0

Submission status: Wrong Answer

Solution code:
n=int(input())
a=list(map(int,input().split()))
mod=10**9+7
from math import gcd
ans=a[0]
for i in range(1,n):
  ans=ans*(a[i]//gcd(ans,a[i]))%mod
s=0
for j in range(n):
  s+=int(ans/a[j]+10**(-9))%mod
print(s%mod)

Submission status: Wrong Answer

Solution code:
n=int(input())
a=list(map(int,input().split()))
mod=10**9+7
from math import gcd
ans=a[0]
for i in range(1,n):
  ans=ans*(a[i]//gcd(ans,a[i]))%mod
s=0
for j in range(n):
  s+=int(ans/a[j])%mod
print(s%mod)