Reverse and Swap

3000ms

262144K

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:

$$$Replace(x, k)$$$ — 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.

Input:

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:

Print the answer for each $$$Sum$$$ query.

Sample Input:

Sample Output:

Sample 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

Sample Output:

29
22
1

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:

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

Informação

Provedor Codeforces

Código CF1401F