CF1401F.Reverse and Swap

You are given an array $a$ of length $2^n$ . You should process $q$ queries on it. Each query has one of the following $4$ types:

1. $Replace(x, k)$ — change $a_x$ to $k$ ;
2. $Reverse(k)$ — reverse each subarray $[(i-1) \cdot 2^k+1, i \cdot 2^k]$ for all $i$ ( $i \ge 1$ );
3. $Swap(k)$ — swap subarrays $[(2i-2) \cdot 2^k+1, (2i-1) \cdot 2^k]$ and $[(2i-1) \cdot 2^k+1, 2i \cdot 2^k]$ for all $i$ ( $i \ge 1$ );
4. $Sum(l, r)$ — print the sum of the elements of subarray $[l, r]$ .

Write a program that can quickly process given queries.

The first line contains two integers $n$ , $q$ ( $0 \le n \le 18$ ; $1 \le q \le 10^5$ ) — the length of array $a$ and the number of queries.

The second line contains $2^n$ integers $a_1, a_2, \ldots, a_{2^n}$ ( $0 \le a_i \le 10^9$ ).

Next $q$ lines contains queries — one per line. Each query has one of $4$ types:

• " $1$ $x$ $k$ " ( $1 \le x \le 2^n$ ; $0 \le k \le 10^9$ ) — $Replace(x, k)$ ;
• " $2$ $k$ " ( $0 \le k \le n$ ) — $Reverse(k)$ ;
• " $3$ $k$ " ( $0 \le k < n$ ) — $Swap(k)$ ;
• " $4$ $l$ $r$ " ( $1 \le l \le r \le 2^n$ ) — $Sum(l, r)$ .

It is guaranteed that there is at least one $Sum$ query.

Print the answer for each $Sum$ query.

In the first sample, initially, the array $a$ is equal to $\{7,4,9,9\}$ .

After processing the first query. the array $a$ becomes $\{7,8,9,9\}$ .

After processing the second query, the array $a_i$ becomes $\{9,9,7,8\}$

Therefore, the answer to the third query is $9+7+8=24$ .

In the second sample, initially, the array $a$ is equal to $\{7,0,8,8,7,1,5,2\}$ . What happens next is:

1. $Sum(3, 7)$ $\to$ $8 + 8 + 7 + 1 + 5 = 29$ ;
2. $Reverse(1)$ $\to$ $\{0,7,8,8,1,7,2,5\}$ ;
3. $Swap(2)$ $\to$ $\{1,7,2,5,0,7,8,8\}$ ;
4. $Sum(1, 6)$ $\to$ $1 + 7 + 2 + 5 + 0 + 7 = 22$ ;
5. $Reverse(3)$ $\to$ $\{8,8,7,0,5,2,7,1\}$ ;
6. $Replace(5, 16)$ $\to$ $\{8,8,7,0,16,2,7,1\}$ ;
7. $Sum(8, 8)$ $\to$ $1$ ;
8. $Swap(0)$ $\to$ $\{8,8,0,7,2,16,1,7\}$ .