Long Jumps
Description
Polycarp found under the Christmas tree an array $a$ of $n$ elements and instructions for playing with it:
- At first, choose index $i$ ($1 \leq i \leq n$) — starting position in the array. Put the chip at the index $i$ (on the value $a_i$).
- While $i \leq n$, add $a_i$ to your score and move the chip $a_i$ positions to the right (i.e. replace $i$ with $i + a_i$).
- If $i > n$, then Polycarp ends the game.
For example, if $n = 5$ and $a = [7, 3, 1, 2, 3]$, then the following game options are possible:
- Polycarp chooses $i = 1$. Game process: $i = 1 \overset{+7}{\longrightarrow} 8$. The score of the game is: $a_1 = 7$.
- Polycarp chooses $i = 2$. Game process: $i = 2 \overset{+3}{\longrightarrow} 5 \overset{+3}{\longrightarrow} 8$. The score of the game is: $a_2 + a_5 = 6$.
- Polycarp chooses $i = 3$. Game process: $i = 3 \overset{+1}{\longrightarrow} 4 \overset{+2}{\longrightarrow} 6$. The score of the game is: $a_3 + a_4 = 3$.
- Polycarp chooses $i = 4$. Game process: $i = 4 \overset{+2}{\longrightarrow} 6$. The score of the game is: $a_4 = 2$.
- Polycarp chooses $i = 5$. Game process: $i = 5 \overset{+3}{\longrightarrow} 8$. The score of the game is: $a_5 = 3$.
Help Polycarp to find out the maximum score he can get if he chooses the starting index in an optimal way.
The first line contains one integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases. Then $t$ test cases follow.
The first line of each test case contains one integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the length of the array $a$.
The next line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \leq a_i \leq 10^9$) — elements of the array $a$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
For each test case, output on a separate line one number — the maximum score that Polycarp can get by playing the game on the corresponding array according to the instruction from the statement. Note that Polycarp chooses any starting position from $1$ to $n$ in such a way as to maximize his result.
Input
The first line contains one integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases. Then $t$ test cases follow.
The first line of each test case contains one integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the length of the array $a$.
The next line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \leq a_i \leq 10^9$) — 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, output on a separate line one number — the maximum score that Polycarp can get by playing the game on the corresponding array according to the instruction from the statement. Note that Polycarp chooses any starting position from $1$ to $n$ in such a way as to maximize his result.
Samples
4
5
7 3 1 2 3
3
2 1 4
6
2 1000 2 3 995 1
5
1 1 1 1 1
7
6
1000
5
Note
The first test case is explained in the statement.
In the second test case, the maximum score can be achieved by choosing $i = 1$.
In the third test case, the maximum score can be achieved by choosing $i = 2$.
In the fourth test case, the maximum score can be achieved by choosing $i = 1$.