Range Queries and Copies

Your task is to maintain a list of arrays which initially has a single array. You have to process the following types of queries:

Set the value a in array k to x.

Calculate the sum of values in range [a,b] in array k.

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