CF1515H.Phoenix and Bits

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题目描述

Phoenix loves playing with bits — specifically, by using the bitwise operations AND, OR, and XOR. He has $n$ integers $a_1, a_2, \dots, a_n$ , and will perform $q$ of the following queries:

replace all numbers $a_i$ where $l \le a_i \le r$ with $a_i$ AND $x$ ;
replace all numbers $a_i$ where $l \le a_i \le r$ with $a_i$ OR $x$ ;
replace all numbers $a_i$ where $l \le a_i \le r$ with $a_i$ XOR $x$ ;
output how many distinct integers $a_i$ where $l \le a_i \le r$ .

For each query, Phoenix is given $l$ , $r$ , and $x$ . Note that he is considering the values of the numbers, not their indices.

输入格式

The first line contains two integers $n$ and $q$ ( $1 \le n \le 2 \cdot 10^5$ ; $1 \le q \le 10^5$ ) — the number of integers and the number of queries, respectively.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $0 \le a_i < 2^{20}$ ) — the integers that Phoenix starts with.

The next $q$ lines contain the queries. For each query, the first integer of each line is $t$ ( $1 \le t \le 4$ ) — the type of query.

If $t \in \{1, 2, 3\}$ , then three integers $l_i$ , $r_i$ , and $x_i$ will follow ( $0 \le l_i, r_i, x_i < 2^{20}$ ; $l_i \le r_i$ ).

Otherwise, if $t=4$ , two integers $l_i$ and $r_i$ will follow ( $0 \le l_i \le r_i < 2^{20}$ ).

It is guaranteed that there is at least one query where $t=4$ .

输出格式

Print the answer for each query where $t=4$ .

输入输出样例

输入#1

输出#1

3
2
1

输入#2

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

输出#2

5
1
2

说明/提示

In the first example:

For the first query, $2$ is replaced by $2$ AND $2 = 2$ and $3$ is replaced with $3$ AND $2 = 2$ . The set of numbers is $\{1, 2, 4, 5\}$ .
For the second query, there are $3$ distinct numbers between $2$ and $5$ : $2$ , $4$ , and $5$ .
For the third query, $2$ is replaced by $2$ XOR $3 = 1$ , $4$ is replaced by $4$ XOR $3 = 7$ , and $5$ is replaced by $5$ XOR $3 = 6$ . The set of numbers is $\{1, 6, 7\}$ .
For the fourth query, there are $2$ distinct numbers between $1$ and $6$ : $1$ and $6$ .
For the fifth query, $1$ is replaced by $1$ OR $8 = 9$ . The set of numbers is $\{6, 7, 9\}$ .
For the sixth query, there is one distinct number between $8$ and $10$ : $9$ .

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