Pusheen is playing Neko Atsume! She has a lot of toys and has laid them out to maximize her fish income. She wants to know how efficient her layout will be though.

After doing a lot of critical thinking and real-time programming, Pusheen has boiled down the fish income in terms of a single variable - the beauty of the arrangement of toys. She thus defines ~f(x)~ to be the fish income given that her layout has beauty ~x~. After some more computation, Pusheen has realized that for all ~x \le 0~, ~f(x) = 1~. Otherwise, ~f(x) = f\left(\left\lfloor \frac{x}{a} - b \right\rfloor \right) + f\left(\left\lfloor \frac{x}{c} - d \right\rfloor \right)~.

Pusheen has ~Q~ layouts, layout ~i~ having beauty ~x_i~. Compute ~f(x_i)~ for many values of ~x_i~.

Constraints

~1 \le x_i \le 10^9~

~2 \le a, c \le 10^9~

~0 \le b, d \le 10^9~

~1 \le Q \le 10^5~

Input Specification

The first line contains five space-separated integers, ~a~, ~b~, ~c~, ~d~, and ~Q~.

The next ~Q~ lines each contain a single positive integer, ~x_i~.

Output Specification

Output ~Q~ lines, the ~f(x_i)~ values in order.

Sample Input

2 0 2 0 3
1
2
3

Sample Output

2
4
4