Problem Description

Takahashi loves browsing the internet using his browser.

However, he has a habit of opening too many tabs, which often causes his browser to crash.

Takahashi's browser crashes when the number of open tabs exceeds $ L $.

When the browser crashes, it automatically restarts with only $ 1 $ tab open.

Initially, Takahashi's browser has $ 1 $ tab open.

Given the history of Takahashi's actions of "opening a new tab" and "closing a tab", determine how many times Takahashi crashes his browser.

Input Format

The input is given from the standard input in the following format:

$ N $ $ L $ $ S $

• The first line contains an integer $N(1\ ≦\ N\ ≦\ 10^5)$ representing the number of actions Takahashi performed, and an integer $L(1\ ≦\ L\ ≦\ 10^5)$ representing the threshold at which the browser crashes, separated by spaces.
• The second line contains a string $ S $ of $ N $ characters consisting only of + and -, representing the chronological history of Takahashi's actions.
• + indicates opening a new tab, and - indicates closing a tab.
• It is guaranteed that Takahashi will not close a tab when there is only $ 1 $ tab open.

Output Format

Output an integer on a single line representing the number of times Takahashi crashes his browser. End the output with a newline.

Sample Input and Output

Sample Input #1

6 2
+++-++

Sample Output #1

2

Sample Input #2

20 20
++-+-+++--+++++-++++

Sample Output #2

0

Notes/Hints

Sample Explanation 1

• Initially, the number of tabs is $ 1 $.
• After the first operation, the number of tabs is $ 2 $.
• After the second operation, the number of tabs becomes $ 3 $, which is greater than $ L $, so the browser crashes and the number of tabs resets to $ 1 $.
• After the third operation, the number of tabs is $ 2 $.
• After the fourth operation, the number of tabs is $ 1 $.
• After the fifth operation, the number of tabs is $ 2 $.
• After the sixth operation, the number of tabs becomes $ 3 $, which is greater than $ L $, so the browser crashes and the number of tabs resets to $ 1 $.

Thus, the browser crashes a total of $ 2 $ times.

见题面 Input 部分

见题面 Output 部分