Propagation Exam Broadcasting

There is a special exam where n students are seated in a row, numbered from 1 to n. Among them, the student at position c (initially with ability w_c) can update his ability. Each student i has an ability w_i and is assigned a walkie‐talkie with a fixed reception range d_i.

The exam works as follows. When a problem with difficulty x is released, every student who can solve it directly is determined by checking whether

$$w_i \ge x,$$

and these students immediately broadcast their solution. In addition, any student i will also solve the problem if i can receive the broadcast from any student j within his own receiving range, i.e. if there exists some j in the interval

$$[i-d_i,\; i+d_i],$$

such that student j has solved the problem. When a student solves the problem (either directly because w_i is sufficient or indirectly via broadcast), he also broadcasts his solution. This process repeats until no additional student can be activated.

You are given two types of operations:

• 1 x: Query the final number of students who will solve a problem of difficulty x after all possible broadcasts. Formally, define for each student i a value $$f_i=\begin{cases}1 & \text{if } w_i\ge x,\\[5mm]1 & \text{if there exists } j\in [i-d_i,i+d_i] \text{ with } f_j=1,\\[3mm]0 & \text{otherwise.}\end{cases}$$
• 2 x: Update the ability of student c by setting w_c to x.

Your task is to process m operations. For each query operation (type 1), output the total number of students that eventually solve the problem.

## inputFormat

The first line contains three integers n, m, and c (1 ≤ c ≤ n) — the number of students, the number of operations, and the index of the student whose ability can be updated.

The second line contains n integers representing the abilities w₁, w₂, ... , w_n.

The third line contains n integers representing the reception ranges d₁, d₂, ... , d_n.

The following m lines each describe an operation in one of the following two formats:

• 1 x: Query operation for a problem with difficulty x.
• 2 x: Update operation that sets w_c to x.

## outputFormat

For each query operation (lines beginning with 1), output a single integer on a new line — the number of students who will eventually solve the problem.

## sample

5 5 3
3 1 2 4 1
1 0 2 1 1
1 2
2 5
1 4
1 3
1 1

4
3
4
5

$$