Description

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.

5 5 5 3
1 2 3 2 5
1 1
2 4
4 5

5
2
2

Note

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 $3$.