CF1416A k-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 $ .

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.