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