Reverse and Swap

给您一个长度为 $2^n$ 的数组 $a$，您现在需要处理 $q$ 个询问，每个询问是以下 4 种类型之一： 1. $Replace(x, k)$ 把 $a_x$ 修改为 $k$； 2. $Reverse(k)$ 对于每一个 $i(i\ge 1)$ ，把区间 $[(i-1)\cdot 2^k+1, i\cdot 2^k]$ 的元素翻转； 3. $Swap(k)$ 对于每一个 $i(i\ge 1)$ ，交换区间 $[(2i-2)\cdot2^k+1,(2i-1)\cdot2^k]$ 和 $[(2i-1)\cdot2^k+1,2i\cdot2^k]$ 的所有元素； 4. $Sum(l,r)$ 输出区间 $[l,r]$ 中所有元素的和。 您需要写一个能快速处理以上询问的程序。

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.

2 3
7 4 9 9
1 2 8
3 1
4 2 4

24

3 8
7 0 8 8 7 1 5 2
4 3 7
2 1
3 2
4 1 6
2 3
1 5 16
4 8 8
3 0

29
22
1

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\} $ .