A15326. 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 $3$ .