# Cut the Rope

SUST Inter University Pro...
Limits 10s, 512 MB

Fahim is a rope seller. He has a special tool for cutting ropes. But recently this tool is behaving oddly. Everytime he tries to cut some rope, it cuts the rope at a random point from the starting point.

He doesn’t have enough money to repair the machine. As his friend, you need to find the $k$-th smallest rope segment after cutting the rope few times with the machine.

## Input

There will be several test cases.

The first line of the input contains the integer $T$ ($0 < T \le 40$), the number of test cases.

Every test case starts with a value $N$ ($1 < N < 10^{15}$), the length of the rope. And, $Q$ ($1 ≤ Q ≤ 10^5$).

The next $Q$ lines each contain a character ('C' or 'F') and an integer $X$ ($1 ≤ X ≤ 10^{15}$). Each line represents a query.

If the line starts with 'C', then the machine cuts the rope at position $X$.

If the line starts with 'F' then find the length of the $X$-th rope segment, after sorting the ropes by length.

## Output

For every test case, print "Case X:" (where X is the case number) as the first line. Then, for every query that starts with 'F' print the length of the desired rope in a single line.

## Sample

InputOutput
1
10 5
C 4
F 1
F 2
C 9
F 1

Case 1:
4
6
1