You are responsible for a company that produces and distributes Aboreo, an alcoholic beverage valued for the variety in its oplo degree, a component that provides sweetness. Using specialized rays, it is possible to precisely modify the oplo degree of stored bottles. You must develop a system to simulate the state of a warehouse where Aboreo bottles are stored and modified. Initially, the warehouse is empty. A total of $$$q$$$ operations will be performed on the warehouse, each in one of the following forms:
1. '1 x' (Add bottle): A new bottle with an oplo degree of $$$x$$$ ($$$1 \leq x \leq 10^8$$$) is added to the warehouse.
2. '2 x' (Increase oplo): The oplo degree of each bottle in the warehouse increases by $$$x$$$ ($$$-10^8 \leq x \leq 10^8$$$). If the oplo degree of the $$$j$$$-th bottle was $$$v_j$$$ before the operation, it becomes $$$v_j + x$$$ afterward.
3. '3 p q' (Multiply oplo): The oplo degree of each bottle is multiplied by $$$\frac{p}{q}$$$ ($$$-10^8 \leq p, q \leq 10^8$$$, $$$q \neq 0$$$, $$$p \neq 0$$$). If the oplo degree of the $$$j$$$-th bottle was $$$v_j$$$ before the operation, it becomes $$$v_j \cdot \frac{p}{q}$$$ afterward.
4. '4 j' (Query degree): Print the oplo degree of the bottle added in operation $$$j$$$ ($$$1 \leq j \leq i$$$), considering all operations performed up to that point.
Notes:
- The oplo degree may become extremely large, small, negative, or non-integer after operations. - For queries (type 4), it is guaranteed that the oplo degree of the queried bottle is an integer $$$0 \leq v \leq 10^8$$$, avoiding precision issues
Implement an algorithm that performs this simulation efficiently.
The input begins with an integer $$$q$$$ indicating the number of operations to perform ($$$2 \leq q \leq 10^5$$$). This is followed by $$$q$$$ lines, each describing an operation in one of the following formats:
- '1 x': Add a new bottle with oplo degree $$$x$$$ ($$$1 \leq x \leq 10^8$$$).
- '2 x': Increase the oplo degree of all bottles by $$$x$$$ ($$$-10^8 \leq x \leq 10^8$$$).
- '3 p q': Multiply the oplo degree of all bottles by $$$\frac{p}{q}$$$ ($$$-10^8 \leq p, q \leq 10^8$$$, $$$q \neq 0$$$, $$$p \neq 0$$$).
- '4 j': Query the oplo degree of the bottle added in operation $$$j$$$ ($$$1 \leq j \leq i$$$, where $$$i$$$ is the current operation number).
Additional constraints:
- There will be at least one operation of type 4 (query). - For type 4 operations, the oplo degree of the queried bottle is guaranteed to be an integer $$$0 \leq v \leq 10^8$$$. Additionally, operation $$$j$$$ is always of type 1 (add bottle).
For each operation of type '4 j', print a single line containing an integer representing the oplo degree of the bottle added in operation $$$j$$$, after applying all operations up to that point.
71 33 1 21 12 13 4 14 14 3
10 8
41 12 -63 3 -54 1
3
In the first example, the following operations are performed in this order:
- A bottle arrives with an oplo degree of $$$3$$$.
- The oplo degree of all bottles is multiplied by $$$\frac{1}{2}$$$. The bottle added in the first operation now has an oplo degree of $$$\frac{3}{2}$$$.
- A bottle arrives with an oplo degree of $$$1$$$.
- The oplo degree of all bottles is increased by $$$1$$$.
- The oplo degree of all bottles is multiplied by $$$4$$$.
- Finally, the oplo degree of the bottle added in the first operation and the bottle added in the third operation must be printed.
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