A14006 | Long Jumps

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.