I I U P C 2 0 1 3 |
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Problem A: See Emily Play |
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You are taking care of Emily this afternoon. To keep her entertained, you've designed a game for her involving some math. The rule for the game is such -- Emily is initially given a big number N. In each step she is supposed to:
For example, starting with 14, she gets 7, 6, 3, 2, 1, 0
Now, you see, Emily is just a kid and hasn’t grown strong notions of rules yet. So, as you have given the rules to her, Emily tries, but misunderstands. In her mind, she rewrites the rules :
For each division Emily takes d seconds, For each subtraction she takes s seconds, for each addition she takes a seconds. Now that you know how she is bending the rules, you start to wonder how many seconds you have to see Emily play.
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Input |
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First line of input will contain the number of test cases, T ≤ 100000. Then T test cases follow. For each case there will be a single line containing four integers separated by space :
N d s a where , 1 ≤ N ≤ 1000000 1 ≤ d, s, a ≤ 10
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Output |
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For each case output a single line containing one real number, the expected number of seconds : T. Show exactly 3 digits after decimal point, properly rounded.
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Sample Input |
Output for Sample Input |
6 1 1 1 1 2 1 1 1 3 1 1 1 4 1 1 1 5 1 1 1 1000000 1 1 1
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3.000 4.000 5.500 5.000 6.750 29.367 |
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Problem Setter : Pratyai Mazumder Alternate Solution : Md. Mahbubul Hasan, Prasanjit Barua |