Problem Statement

You are given a list of positive integers ~a~ of length ~n~. Each integer represents the distance a trampoline will send you to the right. In particular, if you stand on the ~i^{th}~ integer, then you will bounce to coordinate ~i + a_i~ (this will keep happening until you bounce past all the trampolines).

You are asked to perform operations of the following form.

• Type 1: ~1~ ~i~ ~x~ - Adjust the ~i^{th}~ trampoline to bounce ~x~ to the right. OR
• Type 2: ~2~ ~i~ - Determine the number of bounces before you make it past all the trampolines if you started on the ~i^{th}~ trampoline.

After adjusting a trampoline, the trampoline will be adjusted permanently and all future operations should take that into account.

Input Statement

Your first line will contain ~n~ and ~q~, representing the length of ~a~ and the number of operations respectively. Your next line will contain ~n~ space-separated integers representing the values of ~a~. Your next ~q~ lines will contain ~2~ or ~3~ integers each, representing the operations described. If the line starts with a ~1~, then you will receive ~3~ integers, ~1~, ~i~, and ~x~. If the line starts with a ~2~, then you will receive ~2~ integers, ~2~ and ~i~.

Output Statement

For each type 2 query, you should output a new line with an integer, representing the number of bounces before you make it past all the trampolines for the corresponding type 2 operation.

You should output these in the order the operations occurred in the input.

Constraints

• ~1 \leq n \leq 10^4~
• ~1 \leq q \leq 10^4~
• Queries are ~1~-indexed.
• ~1 \leq a_i \leq 10^4~

Sample Cases

Input 1

10 7
1 1 1 1 1 1 1 1 1 1
1 1 5
2 1
2 2
1 1 1
2 1
1 5 10000
2 3

Output 1

6
9
10
3

Explanation 1

The array is initially: 1 1 1 1 1 1 1 1 1 1 After performing 1 1 5 it becomes: 5 1 1 1 1 1 1 1 1 1 After querying 2 1, we know it will take 6 jumps to exit the trampolines: You start at 1, jump to 6, then to 7, then to 8, then to 9, then to 10, then past the trampolines. After querying 2 2 we know that it will take 9 jumps, (jump 1 to the right every time starting from the ~2^{nd}~ trampoline). The rest of the operations follow...