Description

Consider the AC circuit below. We will assume that the circuit is in steady-state. Thus, the voltage at nodes 1 and 2 are given by v

₁

= V

_S

cos

w

t and v

₂

= V

_R

cos (

w

t +

q

) where V

_S

is the voltage of the source,

w

is the frequency (in radians per second), and t is time. V

_R

is the magnitude of the voltage drop across the resistor, and

q

is its phase.

You are to write a program to determine V_R

for different values of

w

. You will need two laws of electricity to solve this problem. The first is Ohm's Law, which states v

₂

= iR where i is the current in the circuit, oriented clockwise. The second is i = C d/dt (v

₁

-v

₂

) which relates the current to the voltage on either side of the capacitor. "d/dt"indicates the derivative with respect to t.

Input

The input will consist of one or more lines. The first line contains three real numbers and a non-negative integer. The real numbers are V

_S

, R, and C, in that order. The integer, n, is the number of test cases. The following n lines of the input will have one real number per line. Each of these numbers is the angular frequency,

w

.

Output

For each angular frequency in the input you are to output its corresponding V

_R

on a single line. Each V

_R

value output should be rounded to three digits after the decimal point.

1.0 1.0 1.0 9
0.01
0.031623
0.1
0.31623
1.0
3.1623
10.0
31.623
100.0

0.010
0.032
0.100
0.302
0.707
0.953
0.995
1.000
1.000

Source

Greater New York 2001