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!

尤金送给布伦卡一个长度为 $n$ 的数组 $a$ 作为生日礼物，其中每个元素都是从 $1$ 到 $m$ 的整数。布伦卡知道尤金非常喜欢互质整数（即两个整数 $x$ 和 $y$ 的唯一公共因数为 $1$），因此她打算向尤金提出 $q$ 个关于该数组的问题。

每次，布伦卡会选择数组 $a$ 的一个子段 $a_l, a_{l + 1}, \ldots, a_r$，并计算这些数的乘积 $p = a_l \cdot a_{l + 1} \cdot \ldots \cdot a_r$。接着，她会请尤金计算在 $1$ 到 $C$（含端点）之间与 $p$ 互质的整数的个数。

请帮助尤金回答所有这些问题！

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 $r$ ($1 \leq l \leq r \leq n$).

输入的第一行包含四个整数 $n$、$m$、$C$、$q$（$1 \leq n, q \leq 10^5$，$1 \leq m \leq 2\cdot 10^4$，$1 \leq C \leq 10^5$）——分别表示数组 $a$ 的长度、$a_{i}$ 的最大可能值、数值 $C$ 以及查询次数。

第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \leq a_{i} \leq m$）——即数组 $a$。

接下来 $q$ 行给出查询。每个查询包含两个整数 $l$ 和 $r$（$1 \leq l \leq r \leq n$）。

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

输出 $q$ 个整数——即布伦卡各个查询的答案。

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 $3$.

以下是该示例的解释：

1. 在第一个查询中，乘积等于 $1$，它与 $1,2,3,4,5$ 均互质。
2. 在第二个查询中，乘积等于 $12$，它与 $1$ 和 $5$ 互质。
3. 在第三个查询中，乘积等于 $10$，它与 $1$ 和 $3$ 互质。