Description:
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.
Input Format:
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.
Output Format:
Print the answer for each $$$Sum$$$ query.
Note:
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. $$$Swap(0)$$$ $$$\to$$$ $$$\{8,8,0,7,2,16,1,7\}$$$.