| # 634_C. Factory Repairs |
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| ## Problem Description |
| A factory produces thimbles in bulk. Typically, it can produce up to a thimbles a day. However, some of the machinery is defective, so it can currently only produce b thimbles each day. The factory intends to choose a k-day period to do maintenance and construction; it cannot produce any thimbles during this time, but will be restored to its full production of a thimbles per day after the k days are complete. |
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| Initially, no orders are pending. The factory receives updates of the form di, ai, indicating that ai new orders have been placed for the di-th day. Each order requires a single thimble to be produced on precisely the specified day. The factory may opt to fill as many or as few of the orders in a single batch as it likes. |
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| As orders come in, the factory owner would like to know the maximum number of orders he will be able to fill if he starts repairs on a given day pi. Help the owner answer his questions. |
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| Input |
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| The first line contains five integers n, k, a, b, and q (1 ≤ k ≤ n ≤ 200 000, 1 ≤ b < a ≤ 10 000, 1 ≤ q ≤ 200 000) — the number of days, the length of the repair time, the production rates of the factory, and the number of updates, respectively. |
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| The next q lines contain the descriptions of the queries. Each query is of one of the following two forms: |
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| * 1 di ai (1 ≤ di ≤ n, 1 ≤ ai ≤ 10 000), representing an update of ai orders on day di, or |
| * 2 pi (1 ≤ pi ≤ n - k + 1), representing a question: at the moment, how many orders could be filled if the factory decided to commence repairs on day pi? |
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| It's guaranteed that the input will contain at least one query of the second type. |
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| Output |
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| For each query of the second type, print a line containing a single integer — the maximum number of orders that the factory can fill over all n days. |
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| Examples |
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| Input |
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| 5 2 2 1 8 |
| 1 1 2 |
| 1 5 3 |
| 1 2 1 |
| 2 2 |
| 1 4 2 |
| 1 3 2 |
| 2 1 |
| 2 3 |
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| Output |
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| 3 |
| 6 |
| 4 |
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| Input |
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| 5 4 10 1 6 |
| 1 1 5 |
| 1 5 5 |
| 1 3 2 |
| 1 5 2 |
| 2 1 |
| 2 2 |
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| Output |
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| 7 |
| 1 |
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| Note |
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| Consider the first sample. |
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| We produce up to 1 thimble a day currently and will produce up to 2 thimbles a day after repairs. Repairs take 2 days. |
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| For the first question, we are able to fill 1 order on day 1, no orders on days 2 and 3 since we are repairing, no orders on day 4 since no thimbles have been ordered for that day, and 2 orders for day 5 since we are limited to our production capacity, for a total of 3 orders filled. |
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| For the third question, we are able to fill 1 order on day 1, 1 order on day 2, and 2 orders on day 5, for a total of 4 orders. |
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| ## Contest Information |
| - **Contest ID**: 634 |
| - **Problem Index**: C |
| - **Points**: 1000.0 |
| - **Rating**: 1700 |
| - **Tags**: data structures |
| - **Time Limit**: {'seconds': 4, 'nanos': 0} seconds |
| - **Memory Limit**: 256000000 bytes |
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| ## Task |
| Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases. |
