You are given an initially empty **multiset** $S$, and you need to perform four types of queries on it:
- $(1, x)$: Insert the integer $x$ into $S$.
- $(2, x)$: Remove one occurrence of $x$ from $S$. It is guaranteed that $x$ appears in $S$.
- $(3, x)$: For each element $p$ in $S$, perform the bitwise XOR operation with $x$ (.i.e $p$ to $p \oplus x$).
- $(4, k)$: Find the $k$-th smallest element of $S$ when it is sorted in non-decreasing order. It is guaranteed that $k \le |S|$, where $|S|$ denotes the size of the multiset.
Your task is to implement a solution that can efficiently perform these operations and find the answer for each query of type $4$.
### Input
- The first line contains an integer $q$.
- The next $q$ lines, each line contains 2 integers, a query.
### Output
- Print the answer for each query of type $4$.
### Constraints
- $1 \le q \le 10^5$.
- $1 \le x \le 10^5$.
- $1 \le k$.
### Example
Input:
```
5
1 1
2 1
1 4
1 5
4 2
```
Output:
```
5
```
