CF1439C Greedy Shopping

You are given an array $ a_1, a_2, \ldots, a_n $ of integers. This array is non-increasing. 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 $ . You should process $ q $ queries of two types: - 1 x y: for each shop $ 1 \leq i \leq 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 $ .

The first line contains two integers $ n $ , $ q $ ( $ 1 \leq n, q \leq 2 \cdot 10^5 $ ). The second line contains $ n $ integers $ a_{1},a_{2}, \ldots, a_{n} $ $ (1 \leq a_{i} \leq 10^9) $ — the costs of the meals. It is guaranteed, that $ a_1 \geq a_2 \geq \ldots \geq a_n $ . Each of the next $ q $ lines contains three integers $ t $ , $ x $ , $ y $ ( $ 1 \leq t \leq 2 $ , $ 1\leq x \leq n $ , $ 1 \leq y \leq 10^9 $ ), each describing the next query. It is guaranteed that there exists at least one query of type $ 2 $ .

For each query of type $ 2 $ output the answer on the new line.

In the first query a hungry man will buy meals in all shops from $ 3 $ to $ 10 $ . In the second query a hungry man will buy meals in shops $ 4 $ , $ 9 $ , and $ 10 $ . After the third query the array $ a_1, a_2, \ldots, a_n $ of costs won't change and will be $ \{10, 10, 10, 6, 6, 5, 5, 5, 3, 1\} $ . In the fourth query a hungry man will buy meals in shops $ 2 $ , $ 3 $ , $ 4 $ , $ 5 $ , $ 9 $ , and $ 10 $ . After the fifth query the array $ a $ of costs will be $ \{10, 10, 10, 7, 6, 5, 5, 5, 3, 1\} $ . In the sixth query a hungry man will buy meals in shops $ 2 $ and $ 4 $ .