k-Amazing Numbers
Description
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 $a$.
The first line contains one integer $t$ ($1 \le t \le 1000$) — the number of test cases. Then $t$ test cases follow.
The first line of each test case contains one integer $n$ ($1 \le n \le 3 \cdot 10^5$) — the number of elements in the array. The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le n$) — the elements of the array.
It is guaranteed that the sum of $n$ over all test cases does not exceed $3 \cdot 10^5$.
For each test case print $n$ integers, where the $i$-th integer is equal to the $i$-amazing number of the array.
Input
The first line contains one integer $t$ ($1 \le t \le 1000$) — the number of test cases. Then $t$ test cases follow.
The first line of each test case contains one integer $n$ ($1 \le n \le 3 \cdot 10^5$) — the number of elements in the array. The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le n$) — the elements of the array.
It is guaranteed that the sum of $n$ over all test cases does not exceed $3 \cdot 10^5$.
Output
For each test case print $n$ integers, where the $i$-th integer is equal to the $i$-amazing number of the array.
Samples
3
5
1 2 3 4 5
5
4 4 4 4 2
6
1 3 1 5 3 1
-1 -1 3 2 1
-1 4 4 4 2
-1 -1 1 1 1 1