A |
Erratic
Expansion Input: Standard Input Output: Standard Output |
Piotr found a magical box in heaven. Its magic power is that if you place
any red balloon inside it then, after one hour, it will multiply to form 3 red and
1 blue colored balloons. Then in the next hour, each of the red balloons will
multiply in the same fashion, but the blue one will multiply to form 4 blue
balloons. This trend will continue indefinitely.
The arrangements of the balloons after the 0th, 1st,
2nd and 3rd hour are depicted in the following diagram.
As you can see, a red balloon in the cell (i, j) (that is ith
row and jth column) will multiply to produce 3 red balloons in the cells
(i*2 - 1, j*2 - 1), (i*2 - 1, j*2), (i*2, j*2 - 1) and a blue balloon in the
cell (i*2, j*2). Whereas, a blue balloon in the cell (i, j) will multiply to
produce 4 blue balloons in the cells (i*2 - 1, j*2 - 1), (i*2 - 1, j*2), (i*2,
j*2 - 1) and (i*2, j*2). The grid size doubles (in both the direction) after
every hour in order to accommodate the extra balloons.
In this problem, Piotr is only interested in the count of the red balloons; more specifically, he would like to know the total number of red balloons in all the rows from A to B after Kth hour.
The first line of input is an integer T(T<1000) that
indicates the number of test cases. Each case contains 3 integers K, A
and B. The meanings of these
variables are mentioned above. K will
be in the range [0, 30] and 1 ≤ A ≤ B ≤ 2K.
For each case, output the case number followed by the total number of red
balloons in rows [A, B] after Kth hour.
3 0 1 1 3 1 8 3 3 7 |
Case
1: 1 Case
2: 27 Case
3: 14 |
Problemsetter: Sohel Hafiz, Special Thanks: Md. Mahbubul Hasan