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!

Input

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

Output

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

Note

Here's an explanation for the example:

in the first query, the product is equal to $$$1$$$, which is coprime with $$$1,2,3,4,5$$$.
in the second query, the product is equal to $$$12$$$, which is coprime with $$$1$$$ and $$$5$$$.
in the third query, the product is equal to $$$10$$$, which is coprime with $$$1$$$ and $$$3$$$.

Burenka, an Array and Queries

Examples