Inversion

Time Limit: 4000/2000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Description

Give an array A, the index starts from 1.
Now we want to know $B_{i}= \max\limits_{i\nmid j}A_{j} $ , $i \geq 2$.

Input

The first line of the input gives the number of test cases T; T test cases follow.
Each case begins with one line with one integer n : the size of array A.
Next one line contains n integers, separated by space, ith number is $A_{i}$.

Limits
$T \leq 20$
$2 \leq n \leq 100000$
$1 \leq Ai \leq 1000000000$
$\sum{n} \leq 700000$

Output

For each test case output one line contains n-1 integers, separated by space, ith number is $B_{i+1}$.

Sample Input

2 4 1 2 3 4 4 1 4 2 3

Sample Output

3 4 3 2 4 4

Hint

liuyiding

Source

2017 Multi-University Training Contest - Te

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