A. k-Amazing Numberstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputFor each test case print n integers, where the i-th integer is equal to the i-amazing number of the array.ExampleInput
3
5
1 2 3 4 5
5
4 4 4 4 2
6
1 3 1 5 3 1
Output
-1 -1 3 2 1 
-1 4 4 4 2 
-1 -1 1 1 1 1 

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  
['binary search', 'data structures', 'implementation', 'two pointers', '*1500']