CF1558B Up the Strip

Note that the memory limit in this problem is lower than in others. You have a vertical strip with $ n $ cells, numbered consecutively from $ 1 $ to $ n $ from top to bottom. You also have a token that is initially placed in cell $ n $ . You will move the token up until it arrives at cell $ 1 $ . Let the token be in cell $ x > 1 $ at some moment. One shift of the token can have either of the following kinds: - Subtraction: you choose an integer $ y $ between $ 1 $ and $ x-1 $ , inclusive, and move the token from cell $ x $ to cell $ x - y $ . - Floored division: you choose an integer $ z $ between $ 2 $ and $ x $ , inclusive, and move the token from cell $ x $ to cell $ \lfloor \frac{x}{z} \rfloor $ ( $ x $ divided by $ z $ rounded down). Find the number of ways to move the token from cell $ n $ to cell $ 1 $ using one or more shifts, and print it modulo $ m $ . Note that if there are several ways to move the token from one cell to another in one shift, all these ways are considered distinct (check example explanation for a better understanding).

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In the first test, there are three ways to move the token from cell $ 3 $ to cell $ 1 $ in one shift: using subtraction of $ y = 2 $ , or using division by $ z = 2 $ or $ z = 3 $ . There are also two ways to move the token from cell $ 3 $ to cell $ 1 $ via cell $ 2 $ : first subtract $ y = 1 $ , and then either subtract $ y = 1 $ again or divide by $ z = 2 $ . Therefore, there are five ways in total.