CF627E Orchestra
Description
Paul is at the orchestra. The string section is arranged in an $ r×c $ rectangular grid and is filled with violinists with the exception of $ n $ violists. Paul really likes violas, so he would like to take a picture including at least $ k $ of them. Paul can take a picture of any axis-parallel rectangle in the orchestra. Count the number of possible pictures that Paul can take.
Two pictures are considered to be different if the coordinates of corresponding rectangles are different.
Input Format
N/A
Output Format
N/A
Explanation/Hint
We will use '\*' to denote violinists and '\#' to denote violists.
In the first sample, the orchestra looks as follows:
`
*#
**
` Paul can take a photograph of just the viola, the $ 1×2 $ column containing the viola, the $ 2×1 $ row containing the viola, or the entire string section, for $ 4 $ pictures total.In the second sample, the orchestra looks as follows: `
#*
*#
#*
` Paul must take a photograph of the entire section.In the third sample, the orchestra looks the same as in the second sample.
*#
**
` Paul can take a photograph of just the viola, the $ 1×2 $ column containing the viola, the $ 2×1 $ row containing the viola, or the entire string section, for $ 4 $ pictures total.In the second sample, the orchestra looks as follows: `
#*
*#
#*
` Paul must take a photograph of the entire section.In the third sample, the orchestra looks the same as in the second sample.