Amazing Numbers

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 ⋅ 10^5) — the number of elements in the array. The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n) — the elements of the array.

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

Example

Input

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

inputFormat

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 ⋅ 10^5) — the number of elements in the array. The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n) — the elements of the array.

It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5.

outputFormat

Output

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

Example

Input

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

样例

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

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