Phoenix and Bits
Description
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.
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 $t=4$.
Print the answer for each query where $t=4$.
Input
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 $t=4$.
Output
Print the answer for each query where $t=4$.
Samples
5 6
5 4 3 2 1
1 2 3 2
4 2 5
3 2 5 3
4 1 6
2 1 1 8
4 8 10
3
2
1
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
5
1
2
Note
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 $10$: $9$.