# C. k-Amazing Numbers SOLUTION Codeforces Round #673 (Div. 2)

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## k-Amazing Numbers SOLUTION

You are given an array a consisting of n integers numbered from 1 to n. Let’s define the k-amazing number of the array as the minimum number that occurs in all of the subsegments of the array having length k (recall that a subsegment of a of length k is a contiguous part of a containing exactly k elements). If there is no integer occuring in all subsegments of length k for some value of k, then the k-amazing number is −1.

For each k from 1 to n calculate the k-amazing number of the array a.

Input

The first line contains one integer t (1≤t≤1000) — the number of test cases. Then t test cases follow.

The first line of each test case contains one integer n (1≤n≤3⋅105) — the number of elements in the array. The second line contains n integers a1,a2,…,an (1≤ai≤n) — the elements of the array.

It is guaranteed that the sum of n over all test cases does not exceed 3⋅105.

Output

For each test case print n integers, where the i-th integer is equal to the i-amazing number of the array.

Example

inputCopy

3

5

1 2 3 4 5

5

4 4 4 4 2

6

1 3 1 5 3 1

outputCopy

-1 -1 3 2 1

-1 4 4 4 2

-1 -1 1 1 1 1