# Restore Sequence SOLUTION RESTORE

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### Restore Sequence November Challenge 2020

Alice has a very complex machine ― when fed with a sequence A1,A2,…,AN, it produces a sequence B1,B2,…,BN, where for each valid i, Bi is the largest index j such that Ai divides Aj (since Ai divides itself, such an index always exist). For example, if the machine is fed with A=[2,6,5,3,4], it produces B=[5,2,3,4,5].
FREE CHEGG ACCOUNT :
Alice gave you a sequence B that was produced by the machine. Find an integer sequence A such that when it is fed into the machine, then the machine produces the sequence B. Alice does not like huge integers, so make sure that 1≤Ai≤4⋅106 holds for each valid i.
Input
The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains a single integer N.
The second line contains N space-separated integers B1,B2,…,BN.
Output
For each test case, print a single line containing N space-separated integers A1,A2,…,AN. For each valid i, 1≤Ai≤4⋅106 should hold.
If there are multiple solutions, you may print any of them. It is guaranteed that at least one solution exists.
Constraints
1≤T≤2⋅104
1≤N≤105
1≤Bi≤N for each valid i
the sum of N over all test cases does not exceed 2⋅105
Subtask #1 (20 points): B1,B2,…,BN are pairwise distinct
Subtask #2 (80 points): original constraints
Example Input
2
5
5 2 3 4 5
4
4 4 4 4
Example Output
2 6 5 3 4
2 6 3 12

FREE CHEGG ACCOUNT :
SOLUTION:
for i in range(int(input())):
n=int(input())
arr=[int(x) for x in input().split()]
#print(*arr)
ans=[0 for _ in range(n)]
num=4*int(1e6)
for i in range(n-1,-1,-1):
if arr[i] == i+1:
ans[i]=num
num-=1
else:
ans[i]=ans[arr[i]-1]
print(*ans)