CF1718F Burenka, an Array and Queries

Eugene got Burenka an array $ a $ of length $ n $ of integers from $ 1 $ to $ m $ for her birthday. Burenka knows that Eugene really likes coprime integers (integers $ x $ and $ y $ such that they have only one common factor (equal to $ 1 $ )) so she wants to to ask Eugene $ q $ questions about the present. Each time Burenka will choose a subsegment $ a_l, a_{l + 1}, \ldots, a_r $ of array $ a $ , and compute the product of these numbers $ p = a_l \cdot a_{l + 1} \cdot \ldots \cdot a_r $ . Then she will ask Eugene to count the number of integers between $ 1 $ and $ C $ inclusive which are coprime with $ p $ . Help Eugene answer all the questions!

In the first line of input there are four integers $ n $ , $ m $ , $ C $ , $ q $ ( $ 1 \leq n, q \leq 10^5 $ , $ 1 \leq m \leq 2\cdot 10^4 $ , $ 1 \leq C \leq 10^5 $ ) — the length of the array $ a $ , the maximum possible value of $ a_{i} $ , the value $ C $ , and the number of queries. The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_{i} \leq m $ ) — the array $ a $ . In the next $ q $ lines the queries are given. Each query consists of two integers $ l $ and $ r $ ( $ 1 \leq l \leq r \leq n $ ).

Print $ q $ integers — the answers to Burenka's queries.

Here's an explanation for the example: 1. in the first query, the product is equal to $ 1 $ , which is coprime with $ 1,2,3,4,5 $ . 2. in the second query, the product is equal to $ 12 $ , which is coprime with $ 1 $ and $ 5 $ . 3. in the third query, the product is equal to $ 10 $ , which is coprime with $ 1 $ and $ 3 $ .