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\ndef II():\n\treturn int(sys.stdin.readline())\n \ndef LI():\n\treturn list(map(int, sys.stdin.readline().split()))\n \ndef MI():\n\treturn map(int, sys.stdin.readline().split())\n \ndef SI():\n\treturn sys.stdin.readline().strip()\nt = II()\nfor q in range(t):\n    n = II()\n    a = LI()\n    d = [[] for i in range(n+1)]\n    d2 = [0]*(n+1)\n    dp = [0]*(n+1)\n    for i in range(n):\n        if d2[a[i]] == 0:\n            d2[a[i]] = 1\n            d[a[i]].append(i)\n            dp[a[i]] = i+1\n        else:\n            d2[a[i]]+=1\n            dp[a[i]] = max(dp[a[i]], i-d[a[i]][-1])\n            d[a[i]].append(i)\n    for i in range(n):\n        dp[a[i]] = max(dp[a[i]], n-d[a[i]][-1])\n    ans = [-1]*(n+1)\n    temp = -1\n    for i in range(n+1):\n        if ans[dp[i]] == -1:\n            ans[dp[i]] = i\n    temp = -1\n    for i in range(1,n+1):\n        if ans[i]!=-1:\n            if temp == -1:\n                temp = ans[i]\n            elif ans[i]<temp:\n                temp = ans[i]\n            else:\n                ans[i] = temp\n        else:\n            ans[i] = temp\n    print(*ans[1:])'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14733