CSES - Range Queries and Copies
  • Time limit: 1.00 s
  • Memory limit: 512 MB
Your task is to maintain a list of arrays which initially has a single array. You have to process the following types of queries:
  1. Set the value $a$ in array $k$ to $x$.
  2. Calculate the sum of values in range $[a,b]$ in array $k$.
  3. Create a copy of array $k$ and add it to the end of the list.
Input

The first input line has two integers $n$ and $q$: the array size and the number of queries.

The next line has $n$ integers $t_1,t_2,\ldots,t_n$: the initial contents of the array.

Finally, there are $q$ lines describing the queries. The format of each line is one of the following: "1 $k$ $a$ $x$", "2 $k$ $a$ $b$" or "3 $k$".

Output

Print the answer to each sum query.

Constraints
  • $1 \le n, q \le 2 \cdot 10^5$
  • $1 \le t_i, x \le 10^9$
  • $1 \le a \le b \le n$
Example

Input:
5 6
2 3 1 2 5
3 1
2 1 1 5
2 2 1 5
1 2 2 5
2 1 1 5
2 2 1 5


Output:
13
13
13
15