Cliffs#4641
On the planet Olympia, workers are building a new dam. The construction site is a rectangular area on a plane, measuring 1 \times L meters, with coordinates set as shown in the figure.
To raise the terrain, magical impulse generators are employed. If a generator with strength is placed at the -coordinate , then for each point in the segment [p - H\,;\, p] on the axis, the elevation increases by q - p + H meters across the entire width (i.e., for any from to ). Similarly, for each point in the segment [p\,;\, p + H], the elevation increases by H + p - q meters across the entire width. The landscape remains unchanged at other points (see figure). During construction, workers may need to calculate the volume of the dam above a specified rectangle.
Write a program to help the workers with these calculations.
The first line contains two integers: — the number of operations the workers will perform (1 \leq N \leq 100{,}000), and — the length of the rectangle (1 \leq L \leq 100{,}000). The next lines describe the operations: the first number indicates the operation type, where means placing a magical impulse generator, and means querying a volume.
If the operation is , two integers and follow (0 \leq p \leq L;\ 1 \leq H \leq L), indicating a generator with strength is placed at position on the axis.
If the operation is , two integers and follow (0 \leq A < B \leq L), indicating a query for the volume of the dam above the rectangle from to on the axis, and from to on the axis.
For each operation, output a line with the following information. If the operation is , output the number . If the operation is , output the integer part of the volume of the dam above the rectangle from to on the axis, and from to on the axis, as illustrated in the figure.
Example 1