F. Reverse and Swaptime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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:   Replace(x, k) — change a_x to k;  Reverse(k) — reverse each subarray [(i-1) \cdot 2^k+1, i \cdot 2^k] for all i (i \ge 1);  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);  Sum(l, r) — print the sum of the elements of subarray [l, r]. Write a program that can quickly process given queries.InputThe 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.OutputPrint the answer for each Sum query.ExamplesInput
2 3
7 4 9 9
1 2 8
3 1
4 2 4
Output
24
Input
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
Output
29
22
1
NoteIn 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:   Sum(3, 7) \to 8 + 8 + 7 + 1 + 5 = 29;  Reverse(1) \to \{0,7,8,8,1,7,2,5\};  Swap(2) \to \{1,7,2,5,0,7,8,8\};  Sum(1, 6) \to 1 + 7 + 2 + 5 + 0 + 7 = 22;  Reverse(3) \to \{8,8,7,0,5,2,7,1\};  Replace(5, 16) \to \{8,8,7,0,16,2,7,1\};  Sum(8, 8) \to 1;  Swap(0) \to \{8,8,0,7,2,16,1,7\}. 
2 3
7 4 9 9
1 2 8
3 1
4 2 4

24 
['binary search', 'bitmasks', 'data structures', '*2400']