Easy challenge?

Time Limit: 2000ms

Memory Limit: 256MB

Easy challenge?

Submissions Submit

Do you think yesterday's problem was hard? 
Don't be sad here is an easy problem to encourage you to continue or Ali will be mad at you :)
 
Given an array $a$ for each $i$, find min $j$ such that $(i - j) <= (a_i + a_j$) or print $-1$ if there is no such $j$

Input

The input consists of multiple test cases. The first line contains a single integer $t (1 \le t \le 10^4)$ --- the number of test cases.
The first line of each test case contains one integer $n (1 \le n \le 2 \cdot 10^5)$ --- the number of elements in the array $a$.
The second line of each test case contains $n$ integers $a_1,a_2, \dots ,a_n (-10^9 \le a_i \le 10^9)$ the elements of the array $a$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output

For each test case, print $n$ integers as described in the problem statement. 

Samples

Input	Output
2 5 -1 8 -5 7 -1 6 1 2 -3 4 -5 6 Copy	2 1 2 1 2 1 1 4 1 6 1 Copy

First reorder the equation to be i - a[i] <= j + a[j] instead of i - j <= a[i]+ a[j].
Then store all the values of i - a[i], call it $v$ then sort it.
Now we want for each j from 1 to n to find the first (j + a[j]) that is greater than or equal to $v$
We can make pre-calculate the minimum index j: iterate starting from the end of the vector and store for each value in $v$ the minimum $j$ so far.