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 $t$ ($1 \le t \le 1000$) — 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.


-----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

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\nimport math\ninput = sys.stdin.readline\n\nt = int(input())\nfor _ in range(t):\n    n = int(input())\n    arr = list(map(int, input().split()))\n    \n    S = {}\n    for el in arr:\n        S[el] = [0]\n        \n    for i in range(len(arr)):\n        S[arr[i]].append(i+1)\n        \n    G = {}\n    \n    for key in S:\n        S[key].append(n+1)\n        best = 0\n        for i in range(len(S[key]) - 1):\n            gap = abs(S[key][i] - S[key][i+1])\n            best = max(gap, best)\n        G[key] = best\n        \n    #print(G)\n    B = {}\n    for key in G:\n        l = G[key]\n        if l not in B:\n            B[l] = key\n        else:\n            B[l] = min(B[l], key)\n            \n    ans = []\n    for key in B:\n        ans.append((key, B[key]))\n        \n    ans.sort()\n    \n    pp = []\n    low = 9999999999999999\n    j = 0\n    for i in range(1, n+1):\n        if j<len(ans) and i==ans[j][0]:\n            if ans[j][1] < low:\n                low = ans[j][1]\n            j += 1\n        if low > 10**10:\n            pp.append(-1)\n        else:\n            pp.append(low)\n            \n    print(*pp)\n        \n        \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13963