C |
Scientific
Experiment Input: Standard Input Output: Standard Output |
|
John wants to be a scientist. A first step of becoming
a scientist is to perform experiment. John has decided to experiment with eggs.
He wants to compare the hardness of eggs from different species. He has decided
to use a nearby large multi-storied building for this purpose. For each species
he will try to find the highest floor from which he can drop the egg and it
will not break. The building has (n+1) floors numbered from 0 to n. John has a
book from which he knows that
1. 
If an egg is dropped from the topmost floor, it
will surely break.
2. If an egg is dropped from floor 0, it will not
break.
3. The eggs of same species are of same strength.
That means if any egg breaks when dropped from the kth floor; all the eggs of that species will break if dropped from kth floor.
4.
If an egg is unbroken after
dropping it from any floor, it remains unharmed, that means the strength of the
egg remains same.
5.
To know the status of the
dropped egg John has to go outside the building.
Unfortunately John has a few problems.
·
He can only carry one egg at a time.
·
He can buy eggs from a shop inside the building and an egg costs x cents.
·
To enter the building he has to pay y cents if he has no egg with him and z cents if he carries an egg with
him.
·
He does not want to waste any egg so he will not leave any unbroken egg
on the ground. But if an egg is broken, he leaves it there.
·
If he has an intact egg at the end, he can sell it for x/2
cents. He does not need to enter the
building to sell the egg.
These
problems are not going to tame John’s curious mind. So he has decided to use an
optimal strategy and minimize his cost in the worst case. As John is not a
programmer, he has asked for your help.
Input
Input
starts with a positive integer T (T≤ 50) denoting
the number of cases.
Each
case contains a line with 4 integer n x
y z as described in the statement. You may assume that 1 < n ≤ 1000 and 1 ≤ x, y, z ≤ 105 and x is even.
Output
For each test case, print the case number and the minimized worst case cost.
Sample
Input Output
for Sample Input
|
7 4 2 998 1000 16 2 1000 1000 16 1000 1 1 4 1000 1 1 7 2 2 2 9 2 1 100 11 2 100 1 |
Case 1: 2000 Case 2: 4008 Case 3: 1015 Case 4: 1003 Case 5: 10 Case 6: 24 Case 7: 111 |
Problemsetter: Tanaeem M. Moosa, Special Thanks: Jane
Alam, M. Rahman, D. Kisman
