| # 1439_C. Greedy Shopping |
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| ## Problem Description |
| You are given an array a_1, a_2, …, a_n of integers. This array is non-increasing. |
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| Let's consider a line with n shops. The shops are numbered with integers from 1 to n from left to right. The cost of a meal in the i-th shop is equal to a_i. |
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| You should process q queries of two types: |
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| * 1 x y: for each shop 1 ≤ i ≤ x set a_{i} = max(a_{i}, y). |
| * 2 x y: let's consider a hungry man with y money. He visits the shops from x-th shop to n-th and if he can buy a meal in the current shop he buys one item of it. Find how many meals he will purchase. The man can buy a meal in the shop i if he has at least a_i money, and after it his money decreases by a_i. |
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| Input |
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| The first line contains two integers n, q (1 ≤ n, q ≤ 2 ⋅ 10^5). |
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| The second line contains n integers a_{1},a_{2}, …, a_{n} (1 ≤ a_{i} ≤ 10^9) — the costs of the meals. It is guaranteed, that a_1 ≥ a_2 ≥ … ≥ a_n. |
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| Each of the next q lines contains three integers t, x, y (1 ≤ t ≤ 2, 1≤ x ≤ n, 1 ≤ y ≤ 10^9), each describing the next query. |
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| It is guaranteed that there exists at least one query of type 2. |
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| Output |
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| For each query of type 2 output the answer on the new line. |
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| Example |
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| Input |
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| 10 6 |
| 10 10 10 6 6 5 5 5 3 1 |
| 2 3 50 |
| 2 4 10 |
| 1 3 10 |
| 2 2 36 |
| 1 4 7 |
| 2 2 17 |
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| Output |
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| 8 |
| 3 |
| 6 |
| 2 |
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| Note |
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| In the first query a hungry man will buy meals in all shops from 3 to 10. |
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| In the second query a hungry man will buy meals in shops 4, 9, and 10. |
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| After the third query the array a_1, a_2, …, a_n of costs won't change and will be \{10, 10, 10, 6, 6, 5, 5, 5, 3, 1\}. |
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| In the fourth query a hungry man will buy meals in shops 2, 3, 4, 5, 9, and 10. |
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| After the fifth query the array a of costs will be \{10, 10, 10, 7, 6, 5, 5, 5, 3, 1\}. |
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| In the sixth query a hungry man will buy meals in shops 2 and 4. |
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| ## Contest Information |
| - **Contest ID**: 1439 |
| - **Problem Index**: C |
| - **Points**: 1750.0 |
| - **Rating**: 2600 |
| - **Tags**: binary search, data structures, divide and conquer, greedy, implementation |
| - **Time Limit**: {'seconds': 3, '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. |
