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*1*to*n*.The

*ith*chapter has*arr[i]*problems, numbered from*1*to*n*.Each page can hold up to

*k*problems. Only a chapter's last page of exercises 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.

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

**Example**

```
arr = [4,2]
k=3
```

For example, Lisaβs workbook contains `arr[1]=4`

problems for chapter `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 `1`

. Problem `1`

is on page `1`

, so it is *special*. Page `2`

contains only Chapter `1`

, Problem `4`

, 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 special problem in her workbook.

**Function Description**

Complete the workbook function in the editor below. It should return an integer that represents the number of special problems in the workbook.

workbook has the following parameter(s):

`n`

: an integer that denotes the number of chapters

`k`

: an integer that denotes the maximum number of problems per page

`arr`

: an array of integers that denote the number of problems in each chapter

**Input Format**

The first line contains two integers `n`

and `k`

, the number of chapters and the maximum number of problems per page.

The second line contains `n`

space-separated integers `arr[i]`

where `arr[i]`

denotes the number of problems in the `ith`

chapter.

**Output Format**

Print the number of *special problems* in Lisaβs workbook.

**Sample Input**

```
5 3
4 2 6 1 10
```

**Sample Output**

```
4
```

**Solution- ### Python**

```
def readInts():
return map(int, raw_input().strip().split(' '))
n, k = readInts()
ts = readInts()
# n = 5
# k = 3
# ts = [4, 2, 6, 1, 10]
ans = 0
pageNum = 1
for chapter, problems in enumerate(ts):
pageLeft = k
for problemId in xrange(1, problems+1):
if pageNum == problemId:
ans += 1
pageLeft -= 1
if pageLeft == 0:
pageLeft = k
pageNum += 1
if pageLeft < k:
pageNum += 1
print ans
```

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