Lisa just got a new math workbook. A workbook contains exercise problems, grouped into chapters. Lisa believes a problem to be special if its index (within a chapter) is the same as the page number where it's located. The format of Lisa's book is as follows:

There are $n$ chapters in Lisa's workbook, numbered from $\mbox{1}$ to $n$.
The $i^{\mbox{th}}$ chapter has $arr\left[i\right]$ problems, numbered from $\mbox{1}$ to $arr\left[i\right]$.
Each page can hold up to $\boldsymbol{\mbox{k}}$ problems. Only a chapter's last page of exercises may contain fewer than $\boldsymbol{\mbox{k}}$ 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 $\mbox{1}$.

Given the details for Lisa's workbook, can you count its number of special problems?

Example

$arr=[4,2]$

$k=3$

Lisa's workbook contains $ar r[1]=4$ problems for chapter $\mbox{1}$, and $arr[2]=2$ problems for chapter $2$. Each page can hold $k=3$ problems.

The first page will hold $3$ problems for chapter $\mbox{1}$. Problem $\mbox{1}$ is on page $\mbox{1}$, so it is special. Page $2$ contains only Chapter $\mbox{1}$, Problem $\begin{array}{c}4\end{array}$, so no special problem is on page $2$. Chapter $2$ problems start on page $3$ and there are $2$ problems. Since there is no problem $3$ on page $3$, there is no special problem on that page either. There is $\mbox{1}$ special problem in her workbook.

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

Function Description

Complete the workbook function in the editor below.

workbook has the following parameter(s):

int n: the number of chapters
int k: the maximum number of problems per page
int arr[n]: the number of problems in each chapter

Returns

• int: the number of special problems in the workbook

Input Format

The first line contains two integers $n$ and $\boldsymbol{\mbox{k}}$, the number of chapters and the maximum number of problems per page.

The second line contains $n$ space-separated integers $arr\left[i\right]$ where $arr\left[i\right]$ denotes the number of problems in the $i^{\mbox{th}}$ chapter.

Constraints

$1\leq n,k,ar r[i]\leq100$

Sample Input
STDIN Function
----- --------
5 3 n = 5, k = 3
4 2 6 1 10 arr = [4, 2, 6, 1, 10]

Sample Output
4

Explanation

The diagram below depicts Lisa's workbook with $n=5$ 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 $\begin{array}{c}4\end{array}$ special problems and thus we print the number $\begin{array}{c}4\end{array}$ on a new line.

见题面

见题面