Description:
This is the easy version of the problem. The only difference is that in this version there are no "remove" queries.
Initially you have a set containing one element — $$$0$$$. You need to handle $$$q$$$ queries of the following types:
- + $$$x$$$ — add the integer $$$x$$$ to the set. It is guaranteed that this integer is not contained in the set;
- ? $$$k$$$ — find the $$$k\text{-mex}$$$ of the set.
In our problem, we define the $$$k\text{-mex}$$$ of a set of integers as the smallest non-negative integer $$$x$$$ that is divisible by $$$k$$$ and which is not contained in the set.
Input Format:
The first line contains an integer $$$q$$$ ($$$1 \leq q \leq 2 \cdot 10^5$$$) — the number of queries.
The following $$$q$$$ lines describe the queries.
An addition query of integer $$$x$$$ is given in the format + $$$x$$$ ($$$1 \leq x \leq 10^{18}$$$). It is guaranteed that $$$x$$$ was not contained in the set.
A search query of $$$k\text{-mex}$$$ is given in the format ? $$$k$$$ ($$$1 \leq k \leq 10^{18}$$$).
It is guaranteed that there will be at least one query of type ?.
Output Format:
For each query of type ? output a single integer — the $$$k\text{-mex}$$$ of the set.
Note:
In the first example:
After the first and second queries, the set will contain elements $$$\{0, 1, 2\}$$$. The smallest non-negative number that is divisible by $$$1$$$ and is not contained in the set is $$$3$$$.
After the fourth query, the set will contain the elements $$$\{0, 1, 2, 4\}$$$. The smallest non-negative number that is divisible by $$$2$$$ and is not contained in the set is $$$6$$$.
In the second example:
- Initially, the set contains only the element $$$\{0\}$$$.
- After adding an integer $$$100$$$ the set contains elements $$$\{0, 100\}$$$.
- $$$100\text{-mex}$$$ of the set is $$$200$$$.
- After adding an integer $$$200$$$ the set contains elements $$$\{0, 100, 200\}$$$.
- $$$100\text{-mex}$$$ of the set is $$$300$$$.
- After adding an integer $$$50$$$ the set contains elements $$$\{0, 50, 100, 200\}$$$.
- $$$50\text{-mex}$$$ of the set is $$$150$$$.