Brick by Brick

You are given an an infinite box of bricks where each brick has dimension $a \times b$. By placing bricks side by side, you can construct a rectangle.

You are asked to construct a series of $n$ rectangles. Each rectangle must have some length-to-width ratio $1:m_i$. For each rectangle, determine the minimum number of bricks you'd need to construct such a rectangle.

Input

The first line contains an integer $n$, the number of rectangles you need to construct.

The second line contains two space-integers $a$ and $b$ representing the dimensions of the bricks.

The next $n$ lines each contain a single integer $m_i$ representing the ratio of the rectangle you need to construct.

Output

For each $1 \le i \le n$, output the minimum number of bricks needed to construct a rectangle with a length-to-width ratio of $1:m_i$.

Constraints

• $1 \le a,b \le 1000$
• $1 \le m \le 10^9$

Example 1

3
2 3
1
2
5

6
3
30

Explanation

Each brick has dimension $2 \times 3$.

The first query 1 asks you to construct a rectangle with a length-to-width ratio of $1:1$. We can do this with 6 bricks:

111222
111222
333444
333444
555666
555666

where each distinct number represents a particular brick (for example, all the 1s represent the first brick). This resulting rectangle has dimension $6 \times 6$, which is in a $1:1$ ratio.