"How do you say 'two kilos' in English? -- Dudu, 2015</p>

Dudu always had trouble with measurements and unit conversions. Can you help him?

입력 형식

The input will begin with a line containing 2 numbers x and y meaning that "x of unit A" is equal to "y of unit B". For instance, if A is "kilos" and B is "pounds" one possibility is x = 3.25 and y = 7.165024.</p>

The next line will contain a single integer N, containing the number of conversions to be performed.

Each of the next N lines will be of the form "z q" where z is a number and q is either 'A' or 'B'.

• 1 ≤ N ≤ 100000
• x,y are strictly positive numbers
• z is a nonnegative number

Output N lines with a number each. See the sample input/output for further details.

예제 입력

3.25 7.165024
5
3.25 A
1 A
0 B
2.1 B
0 A

예제 출력

7.165024
2.20462277
0.000000000000000
0.952543913321
0.000000000000000

힌트

Errors smaller than 10^-4 will be considered correct.

• 3.25 A = 7.165024 B
• 1 A = 2.20462277 B
• 0 B = 0 A
• 2.1 B = 0.952543913321 A
• 0 A = 0 B