There are n types of cells in the lab, numbered from 1 to n. These cells are put in a queue, the i-th cell belongs to type i. Each time I can use mitogen to double the cells in the interval [l, r]. For instance, the original queue is {1 2 3 3 4 5}, after using a mitogen in the interval [2, 5] the queue will be {1 2 2 3 3 3 3 4 4 5}. After some operations this queue could become very long, and I can’t figure out maximum count of cells of same type. Could you help me?
The first line contains a single integer t (1 <= t <= 20), the number of test cases.
For each case, the first line contains 2 integers (1 <= n,m<= 50000) indicating the number of cell types and the number of operations.
For the following m lines, each line represents an operation. There are only two kinds of operations: Q and D. And the format is:
“Q l r”, query the maximum number of cells of same type in the interval [l, r];
“D l r”, double the cells in the interval [l, r];
(0 <= r – l <= 10^8, 1 <= l, r <= the number of all the cells)
For each case, output the case number as shown. Then for each query "Q l r", print the maximum number of cells of same type in the interval [l, r].
Take the sample output for more details.