HackerRank: Lisa’s Workbook

Problem

Lisa just got a new math workbook. A workbook contains exercise problems, grouped into chapters.

• There are n chapters in Lisa’s workbook, numbered from 1 to n.
• The i-th chapter has ti problems, numbered from 1 to ti.
• Each page can hold up to k problems. There are no empty pages or unnecessary spaces, so only the last page of a chapter may contain fewer than k problems.
• Each new chapter starts on a new page, so a page will never contain problems from more than one chapter.
• The page number indexing starts at 1.

Lisa believes a problem to be special if its index (within a chapter) is the same as the page number where it’s located. Given the details for Lisa’s workbook, can you count its number of special problems?

Note: See the diagram in the Explanation section for more details.

Input Format

The first line contains two integers n and k — the number of chapters and the maximum number of problems per page respectively.
The second line contains n integers t1,t2,,tn where ti denotes the number of problems in the ii-th chapter.

Constraints

• 1n,k,ti100

Output Format

Print the number of special problems in Lisa’s workbook.

Sample Input

5 3
4 2 6 1 10


Sample Output

4


Explanation

The diagram below depicts Lisa’s workbook with n=chapters and a maximum of k=3 problems per page. Special problems are outlined in red, and page numbers are in yellow squares.

There are 4 special problems and thus we print the number 4 on a new line.

Solution

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